Direct numerical simulation of two-dimensional mixing layer with time-periodic forcing mimicking the input of piezo-film actuator is performed. Three different forcing frequencies (i.e., the natural frequency, its first subharmonic and second sub-harmonic frequencies) are examined. Simplified chemical reactions are also taken into account. We investigate whether mixing is promoted or suppressed using two indices: the momentum thickness and the concentration of chemical product. The momentum thickness indicates that the forcing enhances the development of mixing layer near the inlet and suppresses it in the region right downstream. Instantaneous vorticity fields show that the location where the vortex pairing starts depend on the forcing frequency. The effect of forcing on the mixing layer development strongly depends on its frequency: in particular, the forcing at the second subharmonic frequency is found to suppress the development of mixing layer in a wide region. On the other hand, from the chemical product concentration, mixing is found to be promoted regardless of the forcing frequency. We also investigate how far the control effect lasts. It is revealed that in the downstream region the mixing layer thickness develops linearly regardless of the forcing frequency, which in turn suggests that the present numerical simulation is performed in a computational domain large enough to examine the control effect.