This paper proposes a new technique for the construction of a concrete-beam health indicator based on the Kullback-Leibler divergence (KLD) and deep learning. Health indicator (HI) construction is a vital part of remaining useful lifetime (RUL) approaches for monitoring the health of concrete structures. Through the construction of a HI, the deterioration process can be processed and portrayed so that it can be forwarded to a prediction module for RUL prognosis. The degradation progression and failure can be identified by predicting the RUL based on the situation of the current specimen; as a result, maintenance can be planned to reduce safety risks, reduce financial costs, and prolong the specimen's useful lifetime. The portrayal of deterioration through HI construction from raw acoustic emission (AE) data is performed using a deep neural network (DNN), whose parameters are obtained by pretraining and fine tuning using a stack autoencoder (SAE). Kullback-Leibler divergence, which is calculated between a reference normal-conditioned signal and a current unknown signal, was used to represent the deterioration process of concrete structures, which has not been investigated for the concrete beams so far. The DNN-based constructor then learns to generate HI from raw data with KLD values as the training label. The HI construction result was evaluated with run-to-fail test data of concrete specimens with two measurements: fitness analysis of the construction result and RUL prognosis. The results confirm the reliability of KLD in portraying the deterioration process, showing a large improvement in comparison to other methods. In addition, this method requires no adept knowledge of the nature of the AE or the system fault, which is more favorable than model-based approaches where this level of expertise is compulsory. Furthermore, AE offers in-service monitoring, allowing the RUL prognosis task to be performed without disrupting the specimen's work.