This paper numerically investigates the physical mechanism of flow instability and heat transfer of natural convection in a cavity with thin fin(s). The left and the right walls of the cavity are differentially heated. The cavity is given an initial temperature, and the thin fin(s) is fixed on the hot wall in order to control the heat transfer. The finite volume method and the SIMPLE algorithm are used to simulate the flow. Distributions of the temperature, the pressure, the velocity and the total pressure are obtained. Then, the energy gradient theory is employed to study the physical mechanism of flow instability and the effect of the thin fin(s) on heat transfer. Based on the energy gradient theory, the energy gradient function K represents the characteristic of flow instability. It is observed from the simulation results that the positions where instabilities take place in the temperature contours accord well with those of higher K value, which demonstrates that the energy gradient theory reveals the physical mechanism of flow instability. Furthermore, the effects of the fin length, the fin position, the fin number, and Ra on heat transfer are investigated. It is found that the effect of the fin length on heat transfer is negligible when Ra is relatively high. When there is only one fin, the most efficient heat transfer rate is achieved as the fin is fixed at the middle height of the cavity. The fin blocks heat transfer with a relatively small Ra, but the fin enhances heat transfer with a relatively large Ra. The fin(s) enhances heat transfer gradually with the increase of Ra under the influence of the thin fin(s). Finally, a linear correlation of K-max with Ra is obtained which reveals the physical mechanism of natural convection from different approaches. (C) 2016 Elsevier Ltd. All rights reserved.