setVIsible(false); from within JFrame
public class aClass{
static JTextField USER_NAME;
static JPasswordField PASSWORD;
static JButton submit;

private static class Handler implements ActionListener {
    @Override

    public void actionPerformed(ActionEvent e) {
        String USER_NAME_I = USER_NAME.getText();
        String PASSWORD_I = PASSWORD.getText();

        try {
           Class.forName("sun.jdbc.odbc.JdbcOdbcDriver");
        } catch (ClassNotFoundException ex) {
            Logger.getLogger(aClass.class.getName()).log(Level.SEVERE, null, ex);
        }
        try {
            Connection con = DriverManager.getConnection("jdbc:mysql://localhost:3306/fake",
             /*DB USER_NAME*/       "fakeuname",
             /*DB password*/       "fakepassword");

            Statement st = con.createStatement();
            String FindQuery = "SELECT acc_pass FROM users where acc_name='"+USER_NAME_I+"'";

            //System.out.println(FindQuery);

            ResultSet rs = st.executeQuery(FindQuery);

            if(rs.next())
            {
                String PASSWORD_DB = rs.getString(1);

                if(PASSWORD_DB.equals(PASSWORD_I))
                {
                    //THIS WILL NOT WORK
                    loginFrame.setVisible(false);


                    //do something
                }

                else
                {
                    JOptionPane.showMessageDialog(null,
                            "Wrong Password",
                            "Error",1);
                }//end else

           }//end if (rs.next())
            else
            {
                JOptionPane.showMessageDialog(null,
                        "Wrong Username",
                        "Error",1);
            }//end else

        } catch (SQLException ex)
        {
            Logger.getLogger(aClass.class.getName()).log(Level.SEVERE, null, ex);
        }//end catch (SQLException ex)
    }//end ActionEvent
}//end ActionListener


aClass(){

    JFrame loginFrame = new JFrame("Logon");
    loginFrame.setVisible(true);
    loginFrame.setDefaultCloseOperation(JFrame.DISPOSE_ON_CLOSE);

    USER_NAME = new JTextField(10);
    PASSWORD = new JPasswordField(10);
    loginFrame.setLayout(new GridLayout(0,1));

    JPanel loginPanel = new JPanel();
    loginFrame.add(loginPanel);

    loginPanel.add(new JLabel("User Name: "));
    loginPanel.add(USER_NAME);
    loginPanel.add(new JLabel("Password: "));
    loginPanel.add(PASSWORD);

    submit = new JButton("Submit");
    loginPanel.add(submit);
    submit.addActionListener(new Handler());

 }//end aClass

public static void main(String args[])
{
    new aClass();
}//end main
}//end class