Sometimes when I shower, I do ghusl and then pray afterwards without doing wudhu? Is this permissible?

Wudhu is not required only after wajib ghusl such as janabat and haydh and mustahab ghusl that have been narrated in the hadith which includes Friday ghusl. A complete list of mustahab ghusls is available in the book of laws by Ayatullah Sistani ruling no 633.
Other than these ghusls, every other ghusl requires wudhu before prayers