In this work, using a two dimensional particle in cell-Monte Carlo collision simulation scheme, interaction of two-color ultra-short laser pulses with the molecular hydrogen gas (H2) is examined. The operational laser parameters, i.e., its pulse shape, duration, and waist, are changed and, their effects on the density and kinetic energy of generated electrons, THz electric field, intensity, and spectrum are studied. It is seen that the best pulse shape generating the THz signal radiation with the highest intensity is a trapezoidal pulse, and the intensity of generated THz radiation is increased at the higher pulse durations and waists. For all the operational laser parameters, the maximum value of emitted THz signal frequency always remains lower than 5 THz. The intensity of applied laser pulses is taken about 1014 w/cm2, and it is observed that while a small portion of the gaseous media gets ionized, the radiated THz signal is significant.