Fragmentation dynamics of the molecular ion Na-2(+) irradiated by an intense femtosecond pulse laser is studied using quantum wave packet propagations. It is demonstrated that the pulse duration (20-250 fs) can be used as a control parameter for both the total dissociation probability and the branching ratio between different dissociation channels. This pulse length effect is important when the duration of the pulse is shorter than the vibrational period of the molecular ion in the ground state. The effects of laser intensity (10(11)-3X10(12) W/cm(2)), wavelength (680-780 nm) and initial vibrational level on the dissociation dynamics are also studied.