In supersymmetry (SUSY) the flavor mixing between top-squark (stop) and charm-squark (scharm) induces the flavor-changing neutral-current (FCNC) stop decay $\tilde t_1 \to c \tilde \chi^0_1$. Searching for this decay serves as a probe of soft SUSY breaking parameters. Focusing on the stop pair production followed by the FCNC decay of one stop and the charge-current decay of the other stop, we investigate the potential of detecting this FCNC stop decay at the Fermilab Tevatron, the CERN Large Hadron Collider (LHC) and the next-generation $e^+e^-$ linear collider (LC). We find that this decay may not be accessible at the Tevatron, but could be observable at the LHC and the LC with high sensitivity.