The effective control of two-dimensional material magnetism is a frontier research field. In this work, the influences of in-plane biaxial tension strain on the electronic structure, magnetic properties, and Curie temperature of monolayer NbSi ₂N ₄are investigated by first-principles calculations based on density functional theory and Monte Carlo simulations in the frame of the Heisenberg model. We demonstrate that the monolayer NbSi ₂N ₄has favorable dynamic and thermal stability through the phonon spectral calculations and ab initio molecular dynamics simulations. It is found that the intrinsic monolayer NbSi ₂N ₄is a non-magnetic metal, which can be transformed into a ferromagnetic metal by 1.5% tensile strain. The electronic structure analysis of monolayer NbSi ₂N ₄shows that the ferromagnetism induced by tensile strain is caused by traveling electrons. There is a half-full band at the monolayer NbSi ₂N ₄Fermi level, which is mainly contributed by the dz ²orbital of the Nb atom. When there is no additional strain, the band is spin-degenerate. Tensile strain can make this band more localized, which leads to Stoner instability, resulting in the ferromagnetic ordering of monolayer NbSi ₂N ₄traveling electrons. The stability of the ferromagnetic coupling is enhanced with the increase of the strain degree. The calculation results of the magnetic anisotropy energy show that the strain can make the direction of the easy magnetization axis of the monolayer NbSi ₂N ₄reverse from the vertical direction to the in-plane, and then back to the vertical direction. Furthermore, the strain can significantly increase the Curie temperature of monolayer NbSi ₂N ₄. The Curie temperature of monolayer NbSi ₂N ₄is 18 K at 2% strain and 87.5 K at 6% strain, which is 386% higher than that at 2% strain. Strain engineering can effectively control the magnetic ground state and Curie temperature of single-layer NbSi ₂N ₄. The research results are expected to promote the development of MA ₂ Z ₄materials in the field of mechanical sensing device design and low-temperature magnetic refrigeration.