According to one embodiment, a sheet stacking apparatus comprises a conveyance path, a plurality of stackers, a plurality of gates, a skew sensor, and a control unit. The gates are arranged in a number corresponding to the number of stackers, and guide the sheets from the conveyance path into the stackers, respectively. The skew sensor detects the skew of the sheet conveyed along the conveyance path. The control unit drives a gate corresponding to a stacker, in which the sheet is to be stacked, in accordance with the skew value of the sheet detected by the skew sensor upstream of the gate corresponding to the stacker, in which the sheet is to be stacked, in the direction in which the sheet is conveyed along the conveyance path.