Computational efficiency is a major challenge for evolutionary algorithm (EA)‐based antenna optimisation methods due to the computationally expensive electromagnetic simulations. Surrogate model‐assisted EAs considerably improve the optimisation efficiency, but most of them are sequential methods, which cannot benefit from parallel simulation of multiple candidate designs for further speed improvement. To address this problem, a new method, called parallel surrogate model‐assisted hybrid differential evolution for antenna optimisation (PSADEA), is proposed. The performance of PSADEA is demonstrated by a dielectric resonator antenna, a Yagi‐Uda antenna, and three mathematical benchmark problems. Experimental results show high operational performance in a few hours using a normal desktop 4‐core workstation. Comparisons show that PSADEA possesses significant advantages in efficiency compared to a state‐of‐the‐art surrogate model‐assisted EA for antenna optimisation, the standard parallel differential evolution algorithm, and parallel particle swarm optimisation. In addition, PSADEA also shows stronger optimisation ability compared to the above reference methods for challenging design cases.