The mean-field approximation is used to calculate the phase diagrams of the spin-3/2 random transverse crystal field (RTCF) model. A bimodal distribution of the RTCF is employed in which one of the modes is in competition with the other mode whose strength is adjusted with a controllable parameter alpha. Thus, some sites in the lattice are under the effect of RTCF D-x with probability p and the rest of the sites are under the effect of alpha D-x with 1 - p. The phase diagrams of the model are obtained on the RTCF-temperature planes by varying p on square lattices. Both second-and first-order phase transitions are displayed and thus tricritical points are also observed. The critical end points and end points for the first-order phase transition lines were also found.