Radio map, or pathloss map prediction, is a crucial method for wireless network modeling and management. By leveraging deep learning to construct pathloss patterns from geographical maps, an accurate digital replica of the transmission environment could be established with less computational overhead and lower prediction error compared to traditional model-driven techniques. While existing state-of-the-art (SOTA) methods predominantly rely on convolutional architectures, this paper introduces a hybrid transformer-convolution model, termed RMTransformer, to enhance the accuracy of radio map prediction. The proposed model features a multi-scale transformer-based encoder for efficient feature extraction and a convolution-based decoder for precise pixel-level image reconstruction. Simulation results demonstrate that the proposed scheme significantly improves prediction accuracy, and over a 30% reduction in root mean square error (RMSE) is achieved compared to typical SOTA approaches.