Is There a Guitar Hero Game on PSP? No — But Rock Band Unplugged Is the Alternative

No mainline Guitar Hero game was released on PSP.

What *Was* on PSP (Rhythm Games)

• Guitar Hero: On Tour (2008) — Nintendo DS ONLY (Guitar Grip accessory).
• Rock Band Unplugged (2009) — PSP Exclusive. Developed by Backbone. Touchscreen/buttons for lanes. No peripheral. Excellent setlist (Master Tracks). This is the closest equivalent.
• DJ Max Portable / Clazziquai / Black Square / Technika Tune: Korean arcade-style rhythm. Button-heavy. High difficulty.
• Patapon 1/2/3: Rhythm-strategy hybrid. Unique art, addictive.
• Parappa the Rapper (PS1 Classic): Downloadable.
• Guitar Rock Tour (Gameloft, 2008): Mobile port (iOS/DS/Feature phones). Not on PSP officially.

Why No GH on PSP?

• UMD load times killed rhythm precision.
• No viable peripheral (DS had Grip; PSP had no port for one).
• Activision prioritized DS (higher install base) and home consoles.

Recommendation: Play Rock Band Unplugged on PSP (PPSSPP emulator upscales beautifully). Or Clone Hero (PC, free, custom songs, supports any controller).