The feature of an indirect bandgap of most semiconducting transition metal carbides (MXenes) limits their applications in optoelectronics devices. By means of density functional theory (DFT) calculations, we have found that the transition of indirect-direct bandgap can occur in MXenes with different functional groups and structures under appropriate biaxial strain. The controllable bandgap of MXenes stems from the fact that the electronic states near the Fermi level have different responses to tensile strain. The stress-strain curves and phonon spectra suggest that semiconducting MXenes can maintain their stability during a wide range of strains. Moreover, the optical dielectric constants of MXenes are red-shifted and enhanced continuously via applying tensile strains. The tunable electronic and optical properties of semiconducting MXenes make them promising candidates for the design of optoelectronic devices.