The curvature effect on the burning velocity of highly curved flames has been investigated numerically and theoretically. The cylindrical flame was used and compared with the counterflow flame to extract the curvature effect. The numerical simulation with detailed chemistry for hydrogen/air, methane/air, and propane/air flames showed that the burning velocity was significantly affected by the flame curvature in addition to the flame stretch. This curvature effect increased the burning velocity for mixtures with Le 1, and only had little effect for mixtures with Le ~ 1. In the conventional burning velocity relation derived from the assumptions of small flame curvature and thin flame thickness, this curvature effect has not included. Therefore, the asymptotic analysis without such assumptions was performed to further investigate this additional curvature effect. The analytical results also showed the flame curvature effect and qualitatively agreed with the numerical simulations. This agreement implies that the conventional burning velocity relation missed this additional curvature effect and that this curvature effect was caused by the thermal-diffusive transport dependence on the sub-coordinate location in the flame zone.