Two-dimensional (2D) boron monolayers have been successfully synthesized on silver substrate very recently. Their potential application is thus of great significance. In this work, we explore the possibility of boron monolayers (BMs) as electrocatalysts for hydrogen evolution reaction (HER) by first-principle method. Our calculations show that the BMs are active catalysts for HER with nearly zero free energy of hydrogen adsorption, metallic conductivity and plenty of active sites in the basal plane. The effect of the substrate on the HER activity is further assessed. It is found that the substrate has a positive effect on the HER performance caused by the competitive effect of mismatch strain and charge transfer. The indepth understanding of the structure dependent HER activity is also provided.