Handling motion blur is one of important issues in visual SLAM. For a fast-moving camera, motion blur is an unavoidable effect and it can degrade the results of localization and reconstruction severely. In this paper, we present a unified algorithm to handle motion blur for visual SLAM, including the blur-robust data association method and the fast deblurring method. In our framework, camera motion and 3-D point structures are reconstructed by SLAM, and the information from SLAM makes the estimation of motion blur quite easy and effective. Reversely, estimating motion blur enables robust data association and drift-free localization of SLAM with blurred images. The blurred images are recovered by fast deconvolution using SLAM data, and more features are extracted and registered to the map so that the SLAM procedure can be continued even with the blurred images. In this way, visual SLAM and deblurring are solved simultaneously, and improve each other's results significantly.