The accurate first-principles prediction of the energetic properties of molecules and clusters from efficient semilocal density functionals is of broad interest. Here we study the performance of a non-empirical Tao-Mo (TM) density functional on binding energies and excitation energies of titanium dioxide and water clusters, as well as reaction barrier heights. To make a comparison, a combination of the TM exchange part with the TPSS (Tao–Perdew–Staroverov–Scuseria) correlation functional—called TMTPSS—is also included in this study. Our calculations show that the best binding energies of titanium dioxide are predicted by PBE0 (Perdew–Burke–Ernzerhof hybrid functional), TM, and TMTPSS with nearly the same accuracy, while B3LYP (Beck’s three-parameter exchange part with Lee-Yang-Parr correlation), TPSS, and PBE (Perdew–Burke–Ernzerhof) yield larger mean absolute errors. For excitation energies of titanium and water clusters, PBE0 and B3LYP are the most accurate functionals, outperforming the performance of semilocal functionals due to the nonlocality problem suffered by the latter. Nevertheless, TMTPSS and TM functionals are still good accurate semilocal methods, improving upon the commonly-used TPSS and PBE functionals. We also find that the best reaction barrier heights are predicted by PBE0 and B3LYP, thanks to the nonlocality incorporated into these two hybrid functionals, but TMTPSS and TM are obviously more accurate than SCAN (Strongly Constrained and Appropriately Normed), TPSS, and PBE, suggesting the good performance of TM and TMTPSS for physically different systems and properties.