Using the coherent potential approximation within full-potential local orbital minimum-basis method, we have performed a systematic investigations on the possible martensitic transformation, electronic and magnetic properties for Ti2CoGa1−xCux system. Results show that the system has a potential martensitic transformation and can be synthesized in experiment with exception of Ti2CoCu alloy due to their negative formation energy. Calculated total magnetic moment are in good agreement with the Slater-Pauling rule Mt = Zt − 18, thus the system is ferromagnetic half-metallic material except for Ti2CoCu, which is also confirmed by density of states with the band gap at the Fermi level, a nonmagnetic behavior is observed for Ti2CoCu alloy. In addition, the potential martensitic transition from cubic to non-modulated tetragonal transformation illustrates more stability of martensitic phase with respect to cubic one. Such behavior can be explained by the hybridizations between the d orbitals.