In this paper, we study a delayed almost periodic differential neoclassical growth model with nonlinear depreciation rate. Relying on the theory of almost periodic functions and by making use of the Lyapunov functional approach, some novel criteria for guaranteeing the existence and global exponential stability of positive almost periodic solutions of the studied model are established. Besides, the correctness of the theoretical results is validated by a numerical example. The established theoretical findings supplement and improve the conclusions in the literature.