With the time-dependent perturbation theory, we calculate the response rate of an Unruh-DeWitt particle detector, which is uniformly accelerated in vacuum along a trajectory parallel to a perfectly reflecting boundary. By comparing the results with their counterparts of a detector being inertial or uniformly accelerated in an unbounded vacuum, we discover that the uniformly accelerated motion may induce spontaneous excitation for a detector initially in its ground state, and the presence of the boundary may bring in significant revisions to the transition rates of the detector.