In this paper, the problem on exponential stability analysis of recurrent neural networks with both time-varying delays and general activation functions is considered. Neither the boundedness and the monotony on these activation functions nor the differentiability on the time-varying delays are assumed. By employing Lyapunov functional and the free-weighting matrix method, several sufficient conditions in linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literature, which is demonstrated via an example with simulation.