This presentation introduces a Bayesian framework for predicting material properties based on microstructure images. Researchers in the field of material science frequently face challenges such as limited data, noise, and uncertainties. Due to these challenges, material design is inherently complex and difficult. To address these issues, we propose combining the Bayesian framework with machine learning methods. Specifically, our proposed framework utilizes deep generative models, which have recently gained significant attention in the field of computational material science. An advantage of our framework lies in its ability to handle prediction uncertainty within the Bayesian framework. During the presentation, we will explain the fundamental concepts of our framework and demonstrate its application to a sample problem: predicting mechanical properties from artificial dual-phase steel microstructure images. In addition, we will discuss the differences between our proposed framework and a conventional regression model based on a convolutional neural network.