Conversion of biomass-derived gamma-valerolactone (GVL) to valuable chemicals has been studied extensively, and understanding the reaction mechanism is very valuable for improving turnover rates and selectivities. Here, we report first principles density functional calculations, through which we show in detail the reaction pathways of GVL conversion on a Ru(0001) surface, in good agreement with recent experimental results performed on supported Ru catalysts. We find that (i) GVL undergoes a ring-opening reaction rather easily, and (ii) the rate-limiting step toward the formation of 1,4-pentanediol (1,4-PDO) and 2-pentanol (2-PeOH) is the hydrogenation step. The high energy barrier for this step is caused by a strong interaction between Ru and the unsaturated acyl intermediate that is formed after opening the ring. Among all the primary products, formation of 2-butanol (2-BuOH) has the smallest activation barrier, while the slowest step is C-C bond cleavage in the decarbonylation step. We further show that the same acyl intermediate after ring opening of GVL can also be formed by dehydrogenation of 1,4-PDO with a moderate activation barrier, which suggests that both 2-PeOH and 2-BuOH can also be produced in secondary steps.