The effects of bimodal random crystal field on the phase diagrams and magnetization curves of ferrimagnetic mixed spin-1/2 and spin-3/2 Blume-Capel model are examined by using the effective field theory with correlations for honeycomb lattice. The phase diagrams are obtained on the (Delta,kT/vertical bar J vertical bar), (Delta,T-comp) and (P,kT/vertical bar J vertical bar) planes for given values of p and Delta, respectively. The model exhibits only the second-order phase transitions as in the Blume-Capel model with constant crystal fields. In addition, it was found that the model presents one or two compensation temperatures for appropriate values of random crystal field for given probability in contrast to constant crystal field case. Therefore, it is shown that the random crystal field considerably affects the thermal variations of net and sublattice magnetizations. Crown Copyright (C) 2012 Published by Elsevier B.V. All rights reserved.