We introduce a novel and reliable approach too generate high-energy photon pulse bursts in both the attosecond and zeptosecond regimes ($1\text{as}={10}^{-18}\text{s};1\text{zs}={10}^{-21}\text{s}$), high-energy photon pulse bursts by synergistically exploiting the inherent characteristics of free-electron lasers (FELs) and laser-Compton scattering. Comprehensive numerical simulations confirm the feasibility of the approach. In our Letter, a 4 GeV electron beam, undergoing the FEL process, emits radiation at 0.7 nm and develops a microbunched structure. These microbunches subsequently interact with a 2 ps laser pulse in a head-on Compton scattering configuration. These results demonstrate that under conditions of well-established electron beam microbunching, the proposed method successfully yields high-brightness $\gamma$-photon pulse bursts with durations of approximately 850 zeptoseconds and exhibiting exceptional signal-to-noise ratios, consistent with theoretical expectations. This technique not only paves the way for probing ultrafast nuclear dynamics but also provides unprecedented tools for quantum science research, enabling explorations of phenomena such as the quantum Zeno and anti-Zeno effects.

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• Compton scattering
• Electron beams & optics
• Ultrafast optics
• Ultrashort pulses