Recent experimental breakthroughs open up new opportunities for magnetism in few-atomic-layer two-dimensional (2D) materials, which makes fabrication of new magnetic 2D materials a fascinating issue. Here, we report the growth of monolayer VSe by molecular beam epitaxy (MBE) method. Electronic properties measurements by scanning tunneling spectroscopy (STS) method revealed that the as-grown monolayer VSe has magnetic characteristic peaks in its electronic density of states and a lower work-function at its edges. Moreover, air exposure experiments show air-stability of the monolayer VSe. This high-quality monolayer VSe, a very air-inert 2D material with magnetism and low edge work function, is promising for applications in developing next-generation low power-consumption, high efficiency spintronic devices and new electrocatalysts.