The phase diagrams of the nonequilibrium mixed spin-3/2 and spin-2 Ising ferrimagnetic system on square lattice under a time-dependent external magnetic field are presented by using the Glauber-type stochastic dynamics. The model system consists of two interpenetrating sublattices of spins σ=3/2 and S=2, and we take only nearest-neighbor interactions between pairs of spins. The system is in contact with a heat bath at absolute temperature T abs and the exchange of energy with the heat bath occurs via one-spin flip of the Glauber dynamics. First, we investigate the time variations of average order parameters to find the phases in the system and then the thermal behavior of the dynamic order parameters to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (first- or second-order) phase transitions. The dynamic phase diagrams are presented in two different planes. Phase diagrams contain paramagnetic ( p), ferrimagnetic ( i 1, i 2, i 3) phases, and three coexistence or mixed phase regions, namely i 1+ p, i 2+ p and i 3+ p mixed phases that strongly depend on interaction parameters.