The microwave devices are usually optimized by combining the precise model with global optimization algorithm. However, this method is time-consuming. In order to optimize the microwave devices rapidly, the knowledge-based neural network (KBNN) is used in this paper. Usually, the a priori knowledge of KBNN is obtained by the empirical formulas. Unfortunately, it is difficult to derive the corresponding formulas for the most electromagnetic problems, especially for complex electromagnetic problems; the formula derivation is almost impossible. We use precise mesh model of EM analysis as teaching signal and coarse mesh model as a priori knowledge to train the neural network (NN) by particle swarm optimization (PSO). The NN constructed by this method is simpler than traditional NN in structure which can replace precise model in optimization and reduce the computing time. The results of electromagnetic band-gap (EBG) structures optimally designed by this kind of KBNN achieve increase in the bandwidth and attenuation of the stopband and small passband ripple level which shows the advantages of the proposed KBNN method.