We propose a flexible way to significantly enhance population transfer efficiency with a train of time-separated pump-Stokes pulse pairs when the non-adiabatic coupling between two degenerate adiabatic states exists in a double Λ-type four-level system, where the pump and Stokes pulses in each pair can be applied in either counterintuitive or intuitive order. It is shown that the needed Rabi frequency for achieving complete population transfer can be reduced dramatically with the increase of number of pump-Stokes pulse pairs, which results from temporal constructive quantum interference between the sequential transitions and subsequent coherent accumulation; moreover, an arbitrary coherent superposition between the two lower states can be realized by suitably tuning the Rabi frequency and the time delay between each pump-Stokes pair. The method may find applications in control of chemical reactions, quantum optics, and quantum information processing.