Grain boundary energies (GBEs) in face-centered cubic (fcc) and body-centered cubic (bcc) metals and alloys were investigated using ab initio calculations. We revealed a scaling relationship between the GBEs of the same grain boundary structure in different metals of the same crystal structure and found that the scaling factor may probably be best estimated by the ratio of the low-index surface energy. Appling the scaling relationship, the general GBEs at 0 K were predicted. Furthermore, adopting the Foiles’s method which assumes that the general GBE has the same temperature dependence as the elastic modulus c$_{44}$ [Scr. Mater., 62 (2010) 231–234], the predicted general GBEs at elevated temperatures were found in nice agreement with available experimental data in literature. The present work puts forward an efficient methodology for predicting the general GBEs of metals and alloys, facilitating GB engineering for advanced alloy design.