Using the mean field theory, we investigate the effect of the random crystal-field on both the spin-3/2 and spin-2 Blume-Capel models. Several new features are found including the apparence of new ordered phases at low temperature and consequently rich ground state phase diagrams. At finite temperature, new types of phase diagrams are found. Furthermore, we show that at low temperature, first-order transition lines are terminated by isolated critical points, between the ferromagnetic phases. We also discuss some interesting phenomena such as the existence of compensation and the existence of topologically different types of phase diagrams. The magnetic properties and phase diagrams of this model are presented. The obtained results confirm the existence of new ferri-magnetic phases and consequently the existence of new topologies for the different types of the phase diagrams. Indeed, these phase diagrams present rich varieties of phase transitions with first and second order phase transition lines. These lines are found to be linked by tri-critical points and terminated at isolated critical points. In the case of the spin-2 Blume-Capel model, the interesting finding to emerge consists in the appearance of a new phase, with magnetization (m=3/2), and consequently new types of phase diagrams, divided on topologies depending on the existence of the paramagnetic phase at temperature T=0 K. Finally, the thermal behaviour of the sub-lattices magnetizations, showed the presence of the compensation behaviours for negative values of the crystal-field.