The mixed spin-1 and spin-3/2 Blume-Capel Ising ferrimagnetic system for the central spin with spin-1 is studied on the Bethe lattice using the exact recursion equations. The exact expressions for the magnetization, the quadrupolax moment, the Curie temperature and the free energy axe found and the phase diagrams axe constructed on the Bethe lattice with the coordination numbers q = 3, 4 and 6 for the various values of the single-ion anisotropy constants d(A) = D-A/J for spin-1 and d(B) = D-B/J for spin-3/2. The existence of a tricritical point is investigated for different values of q and the single-ion anisotropy constants. The phase diagrams in the (k(Tc)/J, d(A)) plane for the central spin axe obtained for two different cases; (1) d(A) = d(B) and (2) d(A) is varied for selected values of d(B). The results are compared with those of other approximate methods.