A theoretical method for controlling handedness of preoriented enantiomers starting from an equal mixture of right(R)-handed and left(L)-handed molecules using linearly polarized femtosecond laser pulses is presented. The essence of the method lies in the fact that the molecular handedness of oriented enantiomers is reflected in the direction of the electronic transition moment vector. A pump-dump control scheme via an electronic excited state is considered for controlling molecular handedness in a femtosecond time scale. The direction of the polarization vector of the pump pulse and that of the dump pulse are determined in such a way that there is the largest interaction between the laser and the L-(R-) handed molecules, while the interaction with R-(L-) handed ones vanishes. In the case in which both the pump and dump pulses are independent of each other with no overlap between them, an analytical expression for the yield of molecular handedness is derived by solving the equation of motion of the density matrix. This expression shows that both the pump and dump lasers with pi-pulse area produce the maximum transfer yield of molecular handedness. The effectiveness of the laser control method is demonstrated by numerical simulation of dynamic chirality of pre-oriented H2POSH in a racemic mixture via the first electronic singlet excited state.