In this study, a low-cost space mapping (SM) modeling method with mesh deformation is proposed for microwave components. In this approach, the coarse-mesh model with mesh deformation is developed as the coarse model, and the fine-mesh model is simulated as the fine model. The SM technique establishes the mapping relationship between the coarse-mesh model and the fine-mesh model. This approach enables us to combine the computational efficiency of the coarse model with the accuracy of the fine model. The automatic mesh deformation technology is embedded in the coarse model to avoid the discontinuous change in the electromagnetic response. The proposed model consisting of the coarse model and two mapping modules can represent the features of the fine model more accurately, and predict the electromagnetic response of microwave components quickly. The proposed mesh SM modeling technique is applied to the four-pole waveguide filter. The value for the training and test errors in the proposed model is less than 1%, which is lower than that for the ANN models and the existing SM models trained with the same data. Compared with HFSS software, the proposed model can save about 70% CPU time in predicting a set of 100 data. The results show that the proposed method achieves a good modeling accuracy and efficiency with few training data and a low computational cost.