The effect of random crystal-field on the stationary states of the kinetic spin-3/2 Blume–Capel model is investigated within the framework of the mean-field approach. The Glauber-type stochastic dynamics is used to describe the time evolution of the system which is subject to a time-dependent oscillating external magnetic field. In addition to the well-known phase transitions and the appearance of the partly ferromagnetic phase characterized by the magnetization m= 1 in equilibrium case, a new dynamical regions between the ferromagnetic phases F1/2, F1 and F3/2 are found where F3/2+F1/2,F3/2+F1, F1+F1/2 phases coexist for a weak value of the reduced magnetic field (h). Whereas for higher value of h both solutions ordered F and disordered P phases coexist. Hence we present six types topologies of phase diagrams which exhibit dynamical first-order, second-order transition lines, dynamical tricritical and isolated critical end points. Furthermore, the dynamical thermal behavior magnetizations, susceptibilities and phase space trajectories are given and discussed.