In this study, we present a new hybrid functional denoted as xOPBE, which is optimized at the 6-311+G(2d,p) basis set and designed with a specific aim of providing accurate C-13 chemical shifts. By mixing the Hartree-Fock exchange into the OPBE functional, xOPBE provides a significantly improved overall performance as compared to its parent OPBE functional, while OPBE was shown previously as an excellent functional for C-13 chemical shifts. Even in the case of the 1-adamantyl cation, for which OPBE completely fails in reproducing the experimental results, xOPBE still performs very well with similar accuracy as the standard CCSD(T) method with a large basis set. Our results also demonstrate that xOPBE not only can improve quantitatively the description of the correct assignments given by OPBE but also can revert OPBE's incorrect assignments qualitatively. Thus, we would like to recommend the use of xOPBE for routine evaluations of C-13 chemical shifts.