We presented a study of the influence of on-site Coulomb correlation U and Hund coupling J on the electronic properties of monolayer FeSe in a pair-checkerboard antiferromagnetic (PAFM) state based on Hubbard-corrected density functional theory (DFT + U). The results demonstrated the Hubbard-U have a strong influence on the electronic bands and lattice structure of monolayer FeSe in PAFM state. The in-plane lattice constant changes under U > 1.85 eV has been identified under full structure optimization. Furthermore, the Hund coupling J has significant influence on the electronic bands and exhibits a remarkable orbital selective behavior at U = 0. Additionally, our results also demonstrated the Hund coupling J has a weaker effect on electronic properties of FeSe when U gets larger. These results are useful for elucidating the possible role of correlation strength on the electronics band and magnetic ground state of monolayer FeSe.