We have investigated the structures of silicon nanoribbons on Ag(110) using first principles calculations. The armchair silicon nanoribbons (ASiNRs) and zigzag silicon nanoribbons (ZSiNRs) with different widths are analyzed. The formation energy study shows that the ASiNRs with the width of 16 Å are the most stable structures. These ASiNRs have the structural parameters same as experimental ones. The simulated scanning tunneling microscope (STM) images of these ASiNRs also agree well with the experimental results. Thus, these ASiNRs are supposed to be the nanoribbons grown in experiment. The electronic structures shows that the ASiNRs are metallic, which is in agreement with the experiments.