The effect the diameter of silver nanorod arrays whose distance between the nanorods was uniform at 65 nm have on Surface-enhanced Raman Scattering (SERS) has been studied by varying the diameter from 28 to 51 nm. Nanorod length was fixed at approximately 62 nm, which is the optimum length for SERS by excitation with a 632.8 nm laser line. The transverse and longitudinal modes of the surface plasmon of these silver nanorods were near 400 and 630 nm, respectively. The extinction of the longitudinal mode increased with increasing nanorod diameter, while the transverse mode did not change significantly. High-quality SERS spectra of p-aminothiophenol and benzenethiol adsorbed on the tips of the silver nanorods were observed by excitation with a 632.8 nm laser line. The SERS enhancement increased with increasing nanorod diameter. We concluded that the SERS enhancement increases when the diameter of silver nanorods is increased mainly by increasing the excitation efficiency of the longitudinal mode. The enhancement factor for the silver nanorods with a 51 nm diameter was approximately $2{ imes}10^7$.