Phase separation of a 50:50 binary system composed of two prolate ellipsoids with different axis ratios is investigated through molecular dynamics simulation. The system can be considered as a coarse-grained model of a binary liquid crystal mixture. Phase separation has been detected in the system by changing the density as the control parameter. The system goes through two different phase changes, one being the phase change due to phase separation and the other one due to orientational phase transition. In the latter case coexistence of the two particles results in simultaneous phase transition