Post-stack fault recognition is typically performed based on structural attributes, which, however, frequently exhibit unclear characterization of fault contacts and poor fault continuity. Deep learning can characterize middle- to large-scale faults accurately but has a limited capacity to characterize small-scale ones. This study developed a multi-scale fault characterization algorithm using amplitude gradient clutter based on synchrosqueezing generalized S-transform (SSGST). First, seismic data were decomposed into single-frequency data volumes across different frequency bands in the time-frequency domain. Then, the clutter of the amplitude gradient vectors was computed based on the seismic data volumes of different frequency bands. Finally, multi-scale faults were characterized using seismic data volumes of different frequency bands. The results from both model simulations and practical data demonstrate that the amplitude gradient clutter property derived using SSGST provides can effectively characterize small-scale faults besides large-and medium-scale faults.