Requirements:
- SAPGUI for Java 7.20 rev.5 installer.
- Java for OS X 2014-001 installer.
- Pre-installed Mac OS X Mavericks 10.9.4.
Steps:
- Uninstall currently installed Java version from mac OS X Mavericks
- Restart mac and follow given instructions
- Open ‘system preferences’ > ‘user & groups’ > create ‘new account’
- Logon to the new user.
- Download the mentioned version of “Java for OS X 2014-001”
- Close all running applications/browser
- Install downloaded “Java for OS X 2014-001”
- Install SAP GUI (SAPGUI for Java 7.20 rev 5)
(As per Apple support page, “Java for OS X 2014-001” includes installation improvements, and supersedes all previous versions of Java for OS X. This package installs the same version of Java 6 included in Java for OS X 2013-005) - refer below screen-shot


Restart your mac
- Logon to the 'new user'
- Launch the ‘SAPGUI 7.20rev5.app’.
Enjoy SAPGUI 7.20 on Mac OSX Mavericks...



Hope it will be helpful.
Thank you !