This paper presents a class of neutral-type neural networks with discontinuous activations and mixed delays. By using differential inclusions theory, the non-smooth analysis theory with Lyapunovlike approach, some new sufficient criteria are given to ascertain the existence, uniqueness and globally exponential stability of the almost periodic solution for the addressed neural network system. Some recent results in the literature are generalized and improved. Finally, simulation results of two topical numerical examples are also delineated to demonstrate the effectiveness of our theoretical results.