This paper considers exponential convergence for a class of high-order recurrent neural networks (HRNNs) with continuously distributed delays in the leakage terms (i.e., “leakage delays”). Without assuming the boundedness on the activation functions, some sufficient conditions are derived to ensure that all solutions of this system converge exponentially to zero point by using Lyapunov functional method and differential inequality techniques, which are new and complement previously known results. In particular, we propose a new approach to prove the exponential convergence of HRNNs with continuously distributed delays in the leakage terms. Moreover, an example is given to show the effectiveness of the proposed method and results.