We report the investigation on the nonlinear optical properties of two typical two-dimensional metal-organic frameworks (2D MOFs) - 2D Cu-MOF and Zn-MOF (copper/zinc 1,4-benzene dicarboxylate, CuBDC and ZnBDC) using spatial self-phase modulation (SSPM) and spatial cross-phase modulation (SXPM) methods. It is found that 2D Cu-MOF exhibits a large nonlinear optical coefficient n2=5.2010-11m2/Wandχ3=8.2410−11e.s.u. By contrast, no nonlinear optical effect was observed from 2D Zn-MOF under the same condition. The main reason is the Cu center of Cu-MOF has variable valence electrons and a vacant 3d atom orbit, which can form a conjugated system with organic ligands through the d-π interaction and therefore strengthen the nonlinear optical effect by the delocalization of π electrons. However, the Zn ion of Zn-MOF with fixed valence electrons and fully occupied d orbit makes it hard to produce observable nonlinear optical effect. Furthermore, we demonstrated the ability of 2D Cu-MOF in all-optical spatial light modulation and optical switch based on the principle of SXPM. This work sheds light on the physics of 2D MOFs in all-optical light modulation, providing an insight for rational design of 2D MOFs with high nonlinear optical coefficients in future. © 2020 Elsevier B.V.