In recent years, several two-dimensional (2D) materials with semiconducting electronic properties have been introduced. The ZrSe2 (Zirconium diselenide) is one of the best materials to replace the silicon in nanoelectronics due to its proper bandgap. In this research, we study the electronic properties of the armchair and zigzag ZrSe2 nanoribbons (AZSNRs and ZZSNRs). Moreover, we have investigated the effect of edge passivation of two 3AZSNR and 3ZZSNR (the ribbon width is 3) structures with hydrogen (H) and oxygen (O) atoms and also both of them (H/O) concurrently. By calculating the cohesive energy of all structures, we deduce that all zigzag and armchair structures with different edge passivations are stable and energy favorable. Also the edge passivation with H-O atoms can change the electronic properties of 3ZZSNR structure significantly, and the structure behavior changes from semiconductor to metallic. In the case of the armchair structures, the edge passivated structure with O atoms (3AZSNR-O) is the most stable and feasible to fabricate in nanoscale experiments. These results show that the ZrSe2 nanoribbons with different edge passivations have potential applications in nanoelectronics.