The discovery of strong materials is essential in materials science and engineering. It becomes more significant to the practical applications of two-dimensional (2D) materials. In this study, the mechanical properties of all known 2D titanium carbide-based MXene monolayers have been systematically investigated by means of the density functional theory computations. Both the impacts of the thickness of the MXenes and the surface functionalization have been considered. Our results reveal that the in-plane planar elastic constants, Young's moduli and Shear moduli increase over the thickness. Moreover, they are enhanced by the terminal groups of surface functionalization. And the oxygen terminal group has the largest influence. As a result, the 2D Ti4C3O2 is the strongest one among all 2D titanium carbide-based MXene, which is even stronger than the graphene. Our prediction provides the theoretical foundation for the specific application of MXenes that demands superior mechanical properties.