By utilizing the time-dependent wavepacket method, we studied the population transfer between the electronic states of the Na 2 molecule driven by femtosecond laser pulses. Three electronic states, X 1 g S + , A 1 u S + and 2 1 g P , are taken to be the initial, the intermediate and the target states, respectively. Two classes of calculations are performed for comparison: one is to invoke the rotating wave approximation (RWA), and the other is more accurate calculations without consideration of RWA (non-RWA). It is found that for this three-state-model, the RWA fails to describe the accurate population transfer process in femtosecond-pulse fields and that the adiabatic passage is hard to be constructed in the non-RWA calculations. Based on the non-RWA calculations, we determined a set of laser parameters, including the peak intensity, detuning, pulse duration and time delay, for efficient population transfer.