Metal organic frameworks (MOFs) have gained tremendous attention in the fields of environmental restoration and sustainable energy for their potential use as photocatalyst. Herein, a new two-dimensional (2D) Cu(I)-based MOF material showing a narrow forbidden-band of 2.13 eV was successfully constructed using a visible-light-harvesting anthracene-based bipyridine ligand. The as-prepared MOF demonstrates high chemical stability and could be stable in the pH range 2-13, which is favorable for its potential application in photocatalysis. Photocatalytic experiments demonstrate that this Cu(I)-MOF exhibits high reactivity for reduction of Cr(VI) in water, with 95% Cr(VI) converting to Cr(III) in 10 min by using MeOH as scavenger under visible-light illumination. Furthermore, this MOF could behave as a highly active photocatalyst for H-2 evolution without additional photosensitizers and cocatalyst. Remarkably, the as-prepared MOF shows enhanced photocatalytic Cr(VI) reduction and H-2 evolution performances compared with the pristine light-harvesting ligand under the same conditions. In connection to these, the photocatalytic reaction mechanism has also been probed.