A discrete frequency domain design is presented for anticipatory learning control, and applied to ram velocity profile tracking in injection molding process by virtue of the repetitive nature. Two adjustable parameters, the lead-time and the learning gain, are designed in two steps, in contrast with the continuous counterpart. The monotonic decay of the tracking error is guaranteed by cutting off the frequencies beyond the learnable band with the aids of DFT/IDFT. The tracking performance is theoretically examined in the presence of initial resetting errors and measurement noise. Numerical simulation is conducted to demonstrate the effectiveness of the proposed anticipatory learning control, with the comparison of both P-type and D-type ones.