We present here an experimental study on the growth of CH3NH3PbBr3 crystals by conventional spin coating and simple drop casting methods. We observed directly that under the diffusion-limited regime, large-size cuboids and pyramid-like single crystals were obtained. Single-crystal X-ray diffraction revealed that these crystals were in the Pm-3m cubic crystalline structure phase, with a refined unit size of 5.93 angstrom. Polycrystals with fractal-like or snowflake-like morphologies were grown by spin coating method, on fluorine-doped tin oxide-coated glass substrates, that we referred to as the attachment kinetics-limited regime. Interestingly enough, with the same technique, cuboids CH3NH3PbBr3 single crystals were obtained on bare glass substrates. These single crystals and polycrystals exhibited a very strong photoluminescence effect. This study paves a way for controlled growth of CH3NH3PbBr3 crystals and their advanced optoelectronic applications.