In general, CNN-based inpainting can recover local patterns effectively using convolutional filters, but it may not exploit global correlation fully. On the other hand, transformer-based inpainting can fill in large holes faithfully based on global correlation, rather than local one. In this paper, we propose a novel image inpainting algorithm, called local and global mixture (LGM), to take advantage of the strengths of both approaches and compensate for their weaknesses. The LGM network comprises the local inpainting network (LIN) and the global inpainting network (GIN) in parallel, which are based on convolutional layers and transformer blocks, respectively, and exchange their intermediate results with each other. Furthermore, we develop an error propagation model with a continuous error mask, updated in LIN but used in both LIN and GIN to provide more reliable inpainting results. Extensive experiments demonstrate that the proposed LGM algorithm provides excellent inpainting performance, which indicates the efficacy of the parallel combination of LIN and GIN and the effectiveness of the error propagation model.