A method that enables an industrial robot to accomplish the peg-in-hole task for holes in concrete is proposed. The proposed method involves slightly detaching the peg from the wall, when moving between search positions, to avoid the negative influence of the concrete's high friction coefficient. It uses a deep neural network (DNN), trained via reinforcement learning, to effectively find holes with variable shape and surface finish (due to the brittle nature of concrete) without analytical modeling or control parameter tuning. The method uses displacement of the peg toward the wall surface, in addition to force and torque, as one of the inputs of the DNN. Since the displacement increases as the peg gets closer to the hole (due to the chamfered shape of holes in concrete), it is a useful parameter for inputting in the DNN. The proposed method was evaluated by training the DNN on a hole 500 times and attempting to find 12 unknown holes. The results of the evaluation show the DNN enabled a robot to find the unknown holes with average success rate of 96.1% and average execution time of 12.5 seconds. Additional evaluations with random initial positions and a different type of peg demonstrate the trained DNN can generalize well to different conditions. Analyses of the influence of the peg displacement input showed the success rate of the DNN is increased by utilizing this parameter. These results validate the proposed method in terms of its effectiveness and applicability to the construction industry.