In the current work, we study a Cauchy problem for a time-fractional pseudo-parabolic equation with a globally Lipschitz source term. We prove the unique existence of a mild solution to the problem, by the common Banach fixed point theorem. This solution is then verified that exists globally in time by Gr¨onwall’s inequality. Compare to previous works about the similar issuse, we approach in a way that does not require using weighted spaces. Although our approach share a similar spirit to previous studies, our method seems to be more precise and natural.