The pinning characteristics of a domain wall with a step-like thickness change along the wall is investigated in 0.15-to 0.5-m-thick films with an in-plane anisotropy using micromagnetic simulation based on the Landau-Lifshitz-Gilbert equation. The asymmetric Bloch wall having the structure in which the magnetostatic coupling develops between spins near the step when the wall is pinned shows the bi-directional pinning effect for magnetic fields applied along the magnetic domain. The wall energy of the pinned wall decreases with increasing step depth due to the largely decrease of the exchange energy component. The depinning field for the negative applied fields which drive the wall in the direction of the nongrooved region (thick film region) is considerably larger than that for the positive ones which drive the wall in the direction of the grooved region (thin film region). The depinning fields for both the positive and negative applied fields increase with decreasing film thickness.