Electromagnetic simulation software has become an important tool for antenna design. However, high-fidelity simulation of wideband or ultra-wideband antennas is very expensive. Therefore, antenna optimization design by using an electromagnetic solver may be limited due to its high computational cost. This problem can be alleviated by the utilization of fast and accurate surrogate models. Unfortunately, conventional surrogate models for antenna design are usually prohibitive because training data acquisition is time-consuming. In order to solve the problem, a modeling method named progressive Gaussian process (PGP) is proposed in this study. Specially, when a Gaussian process (GP) is trained, test sample with the largest predictive variance is inputted into an electromagnetic solver to simulate its results. After that, the test sample is added to the training set to train the GP progressively. The process can incrementally increase some important trusted training data and improve the model generalization performance. Based on the proposed PGP, two monopole antennas are optimized. The optimization results show effectiveness and efficiency of the method.