MXenes have emerged as one of the most promising members among the two-dimensional (2D) material family owing to their unique physical-chemical properties and outstanding application prospects. Here, we investigated the unique magnetic properties of Ti2C MXenes monolayer by means of the first-principles calculations combining with the Heisenberg spin Hamiltonian approach. A strain-induced reversible magnetic transition for the Ti2C monolayer could be found in our study. When the strain is applied to the Ti2C monolayer, the magnetic configuration of the Ti2C monolayer transforms from the A-type antiferromagnetic (A-AFM) phase to the ferromagnetic (FM) phase with the biaxial tensile strain larger than 6%. Furthermore, the transition from the A-AFM phase to the FM phase was found to be closely related with the change of the Ti and C atomic magnetic moments. The direct magnetic coupling between Ti and C atoms with the increased Ti and C magnetic moments is able to stabilize the structure due to the weakened superexchange interaction between Ti and C atoms under large tensile strain. This is the underlying driving force for the transition from the A-AFM phase to the FM phase. This work provides a promising pathway to better understand the existence of magnetic reversal behavior in the Ti2C MXenes monolayer and opens the door to future magnetic applications of MXenes.