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The electronic structure of bulk Hybrid Organic-Inorganic Perovskite (HOIP) CH3NH3PbX3 (X = Br and Cl) has been investigated using a computational method based on Density Functional Theory (DFT). The investigation demonstrates that spin splitting is found when a favoured orientation of organic cation is aligned along the [111], the [101] and the [011] directions. We show that Rashba splitting is induced with the anisotropical character of spin polarization in [111] directions, whereas the unidirectional out-of-plane of spin polarizations are achieved in [011] and [101] directions. By employing k ⃗∙p ⃗ perturbation theory based on symmetry consideration, we find a large spin-orbit strength from these splitting. These findings show that the bulk HOIP CH3NH3PbX3 is a promising material for the development of perovskite-based spintronic devices.