The two-dimensional wake produced by a time-periodic pitching foil with the asymmetric geometry is investigated in the present work. Through numerically solving nonlinear Navier–Stokes equations, we discuss the relationship among the kinematics of the prescribed motion, the asymmetric parameter K ranged as 1 ≤ K ≤ 1, and the types of the wakes including the mP+nS wake, the Bénard–von Kármán wake, the reverse Bénard–von Kármán wake, and the deviated wake. Compared with previous studies, we reveal that the asymmetric geometry of a pitching foil directly affects the foil’s wake structures. The numerical results show that the reverse Bénard–von Kármán wake is easily deviated at K < 0, while the symmetry-breaking of the reverse Bénard–von Kármán wake is delayed at K > 0. Through the vortex dynamic method, we understand that the initial velocity of the vortex affected by the foil’s asymmetry plays a key role in the deviation of the reverse Bénard–von Kármán wake. Moreover, we provide a theoretical model to predict the wake deviation of the asymmetric foil.