A new mechanism for generating particle number asymmetry (PNA) has been developed.This mechanism is realized with a Lagrangian including a complex scalar field and a neutral scalar field. The complex scalar carries U(1) charge which is associated with the PNA.  In the spatially flat universe with a time-dependent scale factor, the time evolution of the PNA is computed. We start with an initial condition where only the condensation of the neutral scalar is non-zero.  With the above initial conditions, the PNA vanishes at the initial time and later it is generated through the interaction between the complex scalar and the condensation of the neutral scalar. We investigate the time dependence of the PNA and find that PNA oscillates at the early time and it begins to dump at the later time. The period and the amplitude of the oscillation depend on the mass spectrum of the model, the temperature and the expansion rate of the universe. We discuss the implications of the oscillating behavior of the PNA on scenarios for the generation of the baryon asymmetry of the universe (BAU).