In two-dimensional materials with the many-body quantum states, edges become especially significant for realizing a host of physical phenomena and for potential applications in nanodevices. Here, we report the successful construction of ultra-flat monolayer 1H-phase niobium diselenide (NbSe2) with atomically sharp zigzag edges. Our scanning tunneling microscopy and spectroscopy measurements reveal that such zigzag edges hold intriguing one-dimensional edge states. Moreover, we observe an obvious energy-dependent charge-density-wave (CDW) modulation near the edge, highlighting the significant edge-CDW interference interactions. Our findings provide a comprehensive study of tunable structural and electronic properties at the edges in monolayer NbSe2. More importantly, the edge-CDW interference model can be feasible for other CDW metals, suggesting a promising direction of extending desired edge functionalities.