The pressure dependence of elastic properties of Mo2Ga2C is studied via first-principles calculation. The present investigation shows that differing from other MAX phases, in Mo2Ga2C the [Formula: see text] is larger than [Formula: see text], because of the strong Ga–Ga interlayer bonds along [Formula: see text]-axis. Moreover, under pressure, the [Formula: see text] increases more rapidly, originating from the faster strengthening of Ga–Ga bonds. Interestingly, elastic constants [Formula: see text] soften under high pressure (more than 20 GPa). Especially, the calculated phonon structure demonstrates that transverse acoustic (TA) phonon mode also softens under pressure, implying possible phase transition. The reduction of [Formula: see text] and softening of phonon mode are attributed to significantly weakened Mo–Mo interaction in contrast to the strengthening of Ga–Ga bonds under high pressure. Our present results further indicate that Mo2Ga2C is more ductile under pressure.