COSMOCR: A numerical code for cosmic ray studies in computational cosmology. We present COSMOCR, a numerical code for the investigation of cosmic ray related studies in computational cosmology. The code follows the diffusive shock acceleration, the mechanical and radiative energy losses and the spatial transport of the suprathermal particles in cosmic environment. Primary cosmic ray electrons and ions are injected at shocks according to the thermal leakage prescription. Secondary electrons are continuously injected as a results of p-p inelastic collisions of primary cosmic ray ions and thermal background nuclei. The code consists of a conservative, finite volume method with a power-law sub-grid model in momentum space. Two slightly different schemes are implemented depending on the stiffness of the cooling terms. Comparisons of numerical results with analytical solution for a number of tests of direct interest show remarkable performance of the present code.