[en] The effects of both an exchange anisotropy and a single-ion anisotropy on the phase diagram and magnetization curves of the ferromagnetic mixed spin-3/2 and spin-1/2 Heisenberg model are investigated by the use of an Oguchi approximation. Although the theory is developed for lattices with general coordination number z, we treat in detail numerically the model on the simple cubic lattice (z=6). In particular, some outstanding features are found in the ground-state behaviours of sublattice and total magnetizations. The origin and nature of the ordered phase in the quantum mixed-spin system at the low temperature region are also discussed. - Research Highlights: →We find eigenvalues and eigenvectors of the mixed-spin anisotropic Heisenberg model. →We determine phase diagrams of the mixed-spin quantum Heisenberg and Ising models. →We find difference between the quantum and classical models at low temperatures. →Physically, we ascribe this difference to the quantum fluctuation effects.