Radiation therapy is crucial in cancer treatment. Experienced experts typically iteratively generate high-quality dose distribution maps, forming the basis for excellent radiation therapy plans. Therefore, automated prediction of dose distribution maps is significant in expediting the treatment process and providing a better starting point for developing radiation therapy plans. With the remarkable results of diffusion models in predicting high-frequency regions of dose distribution maps, dose prediction methods based on diffusion models have been extensively studied. However, existing methods mainly utilize CNNs or Transformers as denoising networks. CNNs lack the capture of global receptive fields, resulting in suboptimal prediction performance. Transformers excel in global modeling but face quadratic complexity with image size, resulting in significant computational overhead. To tackle these challenges, we introduce a novel diffusion model, MD-Dose, based on the Mamba architecture for predicting radiation therapy dose distribution in thoracic cancer patients. In the forward process, MD-Dose adds Gaussian noise to dose distribution maps to obtain pure noise images. In the backward process, MD-Dose utilizes a noise predictor based on the Mamba to predict the noise, ultimately outputting the dose distribution maps. Furthermore, We develop a Mamba encoder to extract structural information and integrate it into the noise predictor for localizing dose regions in the planning target volume (PTV) and organs at risk (OARs). Through extensive experiments on a dataset of 300 thoracic tumor patients, we showcase the superiority of MD-Dose in various metrics and time consumption.