OK, this is the code that doesn't minimize to tray when dialog is open:

mainwindow.h:
Qt Code: 
  1. #ifndef MAINWINDOW_H
  2. #define MAINWINDOW_H
  3.  
  4. #include <QMainWindow>
  5. #include <QSystemTrayIcon>
  6. #include <QPushButton>
  7. #include <QEvent>
  8. #include <QMenu>
  9. #include <QAction>
  10.  
  11. class MainWindow : public QMainWindow
  12. {
  13.     Q_OBJECT
  14.     QSystemTrayIcon *trayIcon;
  15.     QMenu *trayContextMenu;
  16.     QAction *actShow;
  17.     QPushButton *button;
  18.     bool dialog_open;
  19.  
  20. public:
  21.     MainWindow(QWidget *parent = 0);
  22.  
  23. protected:
  24.     void changeEvent(QEvent *);
  25.  
  26. private slots:
  27.     void click();
  28.     void trayIcon_activated(QSystemTrayIcon::ActivationReason reason);
  29.     void actShow_Triggered();
  30. };
  31.  
  32. #endif // MAINWINDOW_H
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mainwindow.cpp:
Qt Code: 
  1. #include "mainwindow.h"
  2. #include <QFileDialog>
  3.  
  4. MainWindow::MainWindow(QWidget *parent) :
  5.     QMainWindow(parent)
  6. {
  7.     QPushButton *button = new QPushButton("button", this);
  8.     setCentralWidget(button);
  9.     connect(button,&QPushButton::clicked,
  10.             this,&MainWindow::click);
  11.     trayIcon=new QSystemTrayIcon;
  12.     trayIcon->setIcon(QIcon("hmtimer.png"));
  13.     trayContextMenu=new QMenu;
  14.     actShow=trayContextMenu->addAction(tr("Show"));
  15.     trayIcon->setContextMenu(trayContextMenu);
  16.     connect(actShow,&QAction::triggered,
  17.             this,&MainWindow::actShow_Triggered);
  18.     connect(trayIcon,&QSystemTrayIcon::activated,
  19.             this,&MainWindow::trayIcon_activated);
  20.     dialog_open=false;
  21. }
  22.  
  23. void MainWindow::changeEvent(QEvent *event)
  24. {
  25.     if(event->type()==QEvent::WindowStateChange
  26.             && dialog_open==false){
  27.         if(isMinimized()){
  28.             this->hide();
  29.             trayIcon->show();
  30.         }
  31.     }
  32.     else{
  33.         QMainWindow::changeEvent(event);
  34.     }
  35. }
  36.  
  37. void MainWindow::click()
  38. {
  39.     dialog_open=true;
  40.     QFileDialog::getOpenFileName(this,QString());
  41.     dialog_open=false;
  42. }
  43.  
  44. void MainWindow::trayIcon_activated(QSystemTrayIcon::ActivationReason reason)
  45. {
  46.     if(reason==3){ //reason==Trigger
  47.         this->show();
  48.         trayIcon->hide();
  49.     }
  50. }
  51.  
  52. void MainWindow::actShow_Triggered()
  53. {
  54.     this->show();
  55.     trayIcon->hide();
  56. }
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