One of the important tasks for bridge maintenance is bridge deck crack inspection. Traditionally, a human inspector detects cracks using his/her eyes and finds the location of cracks manually. Thus the accuracy of the inspection result is low due to the subjective nature of human judgement. We propose a system that uses a mobile robot to conduct the inspection, where the robot collects bridge deck images with a high resolution camera. In this method, the Laplacian of Gaussian algorithm is used to detect cracks and the crack map is obtained through camera calibration and robot localization. To ensure that the robot collects all the images on the bridge deck, we develop a complete coverage path planning algorithm for the mobile robot. We compare it with other path planning strategies. Finally, we validate our proposed system through experiments and simulation.