A series of non-transition elements bound to the Ni Σ5 (012) symmetrical tilt grain boundary (GB) and the (012) free surface (FS) systems has been studied by first-principles calculation using WIEN2k code, which is based on the full-potential linearized augmented plane wave method with the generalized gradient approximation. The multilayer relaxations in the presence and absence of solutes are determined by the force minimization procedure. The binding energies at some GB/FS/bulk sites including both interstitial and substitutional sites are calculated for all the non-transition elements between H and Rn (from the first-row to the sixth-row elements). The GB/FS segregation energy is obtained by calculating the binding energy difference between the GB/FS site and the inner bulk site. The embrittling potency energy is obtained by calculating the difference between the GB and FS segregation energies on the basis of the Rice–Wang model. The calculated results show that most of the non-transition elements have negative GB/FS segregation energies. In our definition, this means that there exists a segregation site in the GB/FS that is more stable for the solute atom than in the bulk. The embrittling potency energies are positive for most of the solutes. However, some exceptions such as Be, B, C, and Si having negative and large embrittling potency can enhance the GB cohesion. The calculated results are found to be consistent with the various experimental findings within the discussion based on the simple site competition model neglecting the interactions between different solutes.