An effective and accurate graph matching method is very important in content-based image retrieval systems using graph matching. In this paper, we propose an image retrieval system using a new graph matching algorithm based on Bayes theorem and Dirichlet distribution. To be more specific, each image is represented as a graph using nodes (detectors) and attributes of edges in the graph are assigned using the distance between two descriptors. Then, matching matrix is calculated to indicate the degree of matching between two node sets in different graphs using Bayes theorem and Dirichlet distribution. Last, the proposed algorithm searches for an optimal matching solution using convex relaxation algorithm from matching matrix. Here, we present an image as graph using MSER region detector which is robust to various transformations and calculate matching matrix using SIFT descriptor which is invariant against scale and rotation. Correlation between descriptors of two images is substituted for similarity between two images. Therefore, in retrieval phase, the system selects the images with high similarity by matching query image to each of all images in the database. We used COIL-20 database to test and evaluate the proposed system and compared our system with an image retrieval system using spectral matching method. The experimental results have shown that the proposed system based on a new graph matching algorithm achieves superior performance in comparison with spectral matching method.