The structural, electronic and magnetic properties of Cd1-xMnxTe alloy in the zinc-blende (ZB) phase were studied within the framework of spin-polarized density functional theory using the generalized gradient approximation (GGA). We employed the GGA+ U SIC (GGA method plus self-interaction correction potential), which gives a better description of systems with strong Coulomb correlations of the d-electrons. In this paper, we first discuss implementation of the GGA+U method to the ground state calculations of pure CdTe and ferromagnetic MnTe. The alloys are modelled at selected compositions as ordered structures described in terms of periodically repeated supercells for the compositions of x = 0.25, 0.5, and 0.75. The compositional dependences of the lattice constant, electronic band structure and partial densities of states of the ferromagnetic Cd1-xMnxTe alloy were also studied. We estimated the spin-exchange splitting energies produced by the Mn 3d-states and determined the exchange constants for the conduction and valence bands of the alloy. The energy positions of the occupied and unoccupied Mn 3d-bands in the electronic structure of the ferromagnetic Cd1-xMnxTe alloy are also presented. Our calculations based on the GGA+ U SIC approach agree well with the available experimental data and other calculations.