import javax.swing.*;
import java.awt.*;
import java.awt.event.*;

public class Caculator extends JFrame{
//panel
private Container contentPane;
private JPanel leftPanel;
private JPanel centerPanel;
private JPanel rightPanel;

//TextField
private JTextField imput1TextField;
private JTextField imput2TextField;

//label
private JLabel answerLabel;

//button
private JButton plusButton;
private JButton minusButton;
private JButton mutiplyButton;
private JButton divideButton;

public Caculator(){
super("我的计算器");
contentPane=this.getContentPane();
this.setSize(300,300);

//centering
Dimension frameSize=this.getSize();
Dimension screenSize=Toolkit.getDefaultToolkit().getScreenSize();
this.setLocation((screenSize.width-frameSize.width)/2,(screenSize.height-frameSize.height)/2);

//left
leftPanel=new JPanel();
leftPanel.setLayout(new GridLayout(3,1));
leftPanel.add(new JLabel("数字1"));
leftPanel.add(new JLabel("数字2"));
leftPanel.add(new JLabel("结果是"));
contentPane.add(leftPanel,BorderLayout.WEST);

//center
centerPanel=new JPanel();
centerPanel.setLayout(new GridLayout(3,1));
imput1TextField=new JTextField(10);
imput2TextField=new JTextField(10);
answerLabel=new JLabel();
centerPanel.add(imput1TextField);
centerPanel.add(imput2TextField);
centerPanel.add(answerLabel);
contentPane.add(centerPanel,BorderLayout.CENTER);

//right
    rightPanel=new JPanel();
    rightPanel.setLayout(new GridLayout(2,2));
    plusButton=new JButton("+");
    minusButton=new JButton("-");
    mutiplyButton=new JButton("x");
    divideButton=new JButton("/");
    rightPanel.add(plusButton);
    plusButton.addActionListener(new DoClick());
    rightPanel.add(minusButton);
    minusButton.addActionListener(new DoClick());
    rightPanel.add(mutiplyButton);
    mutiplyButton.addActionListener(new DoClick());
    rightPanel.add(divideButton);
    divideButton.addActionListener(new DoClick());
    contentPane.add(rightPanel,BorderLayout.EAST);
 }
 
    
 //listen
 class DoClick implements ActionListener{
     public void actionPerformed(ActionEvent e){
         Double d1=new Double(imput1TextField.getText()).doubleValue();
     Double d2=new Double(imput2TextField.getText()).doubleValue();
     if (e.getSource()==plusButton) answerLabel.setText(""+(d1+d2));
     else if (e.getSource()==minusButton) answerLabel.setText(""+(d1-d2));
     else if (e.getSource()==mutiplyButton) answerLabel.setText(""+(d1*d2));
     else if (e.getSource()==divideButton) answerLabel.setText(""+(d1/d2));
     }
 }
    
    
  
 public static void main(String args[]){
  Caculator ca=new Caculator();
 }
}
   
编译错误:
--------------------Configuration: j2sdk4.0 --------------------
J:javaCaculator.java:76: incompatible types
found   : double
required: java.lang.Double
         Double d1=new Double(imput1TextField.getText()).doubleValue();
                                                                               ^
J:javaCaculator.java:77: incompatible types
found   : double
required: java.lang.Double
     Double d2=new Double(imput2TextField.getText()).doubleValue();
                                                                                   ^
J:javaCaculator.java:78: operator + cannot be applied to java.lang.Double,java.lang.Double
     if (e.getSource()==plusButton) answerLabel.setText(""+(d1+d2));
                                                                                 ^
J:javaCaculator.java:79: operator - cannot be applied to java.lang.Double,java.lang.Double
     else if (e.getSource()==minusButton) answerLabel.setText(""+(d1-d2));
                                                                                       ^
J:javaCaculator.java:80: operator * cannot be applied to java.lang.Double,java.lang.Double
     else if (e.getSource()==mutiplyButton) answerLabel.setText(""+(d1*d2));
                                                                                         ^
J:javaCaculator.java:81: operator / cannot be applied to java.lang.Double,java.lang.Double
     else if (e.getSource()==divideButton) answerLabel.setText(""+(d1/d2));
                                                                                        ^
6 errors

Process completed.


    

把Double d1=new Double(imput1TextField.getText()).doubleValue();中的Double d1 换成double d1试试看
Double(imput1TextField.getText()).doubleValue()返回的是一个double数值，不能与Double相匹配！

在构造函数末尾加一句
this.setVisible(true);

actionPerformed中
Double改为double 

Double和double不一样的

你看一下你的错误提示，都是Double和double数据类型不符引起的

Double 是 double 的一个wrapper，他们不一样 :)
只有double int才能参与运算，而Integer Double 则不行