Abstract We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, σ = ± 1 2 , alternated with spins that can take the four values, S = ± 3 2 , ± 1 2 . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude ( h) and reduced temperature ( T) plane, and in the reduced temperature and interaction parameter planes, namely in the ( h, T) and ( d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in ( h, T) plane, but do not exhibit in the ( d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the ( d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic ( i) phases, two coexistence or mixed phase regions, (f+p) and ( i+p), that strongly depend on interaction parameters.