The aerodynamic characteristics of the foil undergoing the coexisting of fast and slow pitching have been studied via Immersed Boundary (IB) method. With an adjustable parameter , the foil kinematics is defined by making the period corresponding to the positive amplitude faster than that corresponding to the negative amplitude, and vice versa. An opposite scenario is observed at and , where the positive lift is improved via decreasing at but the negative lift enlarges with increasing at , which is of benefit to generate up-burst and dive of the pitching foil, respectively. The lift generation is investigated with the time history of the lift coefficient and the time-mean streamwise velocity, which renders a physical basis for understanding the behavior of flying animals.