Hello farzin521, Thank you for posting on the Final Fantasy XIV Technical Support Forums.

Yes, you should be able to play on the character you played on PS4. You need to purchase the game for MAC and register the game to your Square-Enix account. When you log into the game everything should be there. We also suggest not playing on a shared network, this can cause problems.
If you have any further questions, you will need to contact the support center directly.

To reach our live chat support please follow the steps below.

1. Visit the SQUARE ENIX Support Center at http://support.na.square-enix.com/
2. Select FINAL FANTASY XIV as the game title.
3. on the next screen click on "Contact".
4. You will then need to select a category and sub category from the drop down menus.
5. Next, type a basic description of your inquiry in the "Contact details" section and click "Next".
6. on the following page click "Next" again. Ignoring any Knowledge Base Suggestions that may apply.
7. Provided your contact is during SQUARE ENIX Support Center's hours of operation, you should see a Chat Support option. Click "proceed to chat support" to initiate contact with one of our Chat Support Representatives.

NOTE: Live service is available Monday through Friday, 9:00 - 18:00 (Pacific Time) (Excluding holidays)

Thank you for playing Final Fantasy XIV! Hope to see you online.