Can You Play Psychonauts on Xbox 360?

Psychonauts on Xbox 360

No. The original Psychonauts (2005) released on original Xbox, not Xbox 360. Psychonauts Remastered (2020) launched on Xbox One/PS4/PC—not backward compatible with Xbox 360.

Options: Find an original Xbox for the 2005 version, or play Remastered on Xbox One/Series X|S/PS4/PS5/PC.