Two dimensional (2D) nanomaterials have demonstrated huge potential in wide applications from nanodevices to energy harvesting/storage. In this work, we propose a new class of 2D monolayers, nitrogen-functionalized MXenes (Nb2CN2 and Ta2CN2), based on density-functional theory (DFT). We find that these monolayers are direct semiconductors with near linear energy dispersions at the Gamma point. M2CN2 monolayers have significant small effective mass and show an ultra-high mobility of up to 106 cm(2) V-1 s(-1). We show that the electronic structures of the M2CN2 monolayers can be easily controlled by biaxial and uniaxial strains. Importantly, the carrier mobility and direct band gap can be dramatically increased within a certain range of strain. A direct-indirect band gap transition can be triggered and the band gap can be tuned under strain. The tunable electronic properties are attributed to the structural changes and charge redistribution under stain. Our findings demonstrate that N-functionalized MXenes are promising materials for nanodevices with high speed and low power.