Real-world computationally expensive design optimization problems with discrete variables pose challenges to surrogate-based optimization methods in terms of both efficiency and search ability. In this paper, a new method is introduced, called surrogate model-aware differential evolution with neighbourhood exploration, which has two phases. The first phase adopts a surrogate-based optimization method based on efficient surrogate model-aware search framework, the goal of which is to reach at least the neighbourhood of the global optimum. In the second phase, a neighbourhood exploration method for discrete variables is developed and collaborates with the first phase to further improve the obtained solutions. Empirical studies on various benchmark problems and a real-world network-on-chip design optimization problem show the combined advantages in terms of efficiency and search ability: when only a very limited number of exact evaluations are allowed, the proposed method is not slower than one of the most efficient methods for the targeted problem; when more evaluations are allowed, the proposed method can obtain results with comparable quality compared to standard differential evolution, but it requires only 1% to 30% of exact function evaluations.