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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.