Most regulations only allow the use of the coarse fraction of recycled concrete aggregate (RCA) for the manufacture of new concrete, although the heterogeneity of RCA makes it difficult to predict the compressive strength of concrete, which is an obstacle to the incorporation of RCA in concrete production. The compressive strength of recycled aggregate concrete is closely related to the dosage of its constituents. This article proposes a novel artificial neural network (ANN) model to predict the 28-day compressive strength of recycled aggregate concrete. The ANN used in this work has 11 neurons in the input layer: the mass of cement, fly ash, water, superplasticizer, fine natural aggregate, coarse natural or recycled aggregate, and their properties, such as: sand fineness modulus of sand, water absorption capacity, saturated surface dry density of the coarse aggregate mix and the maximum particle size. Two training methods were used for the ANN combining 15 and 20 hidden layers: Levenberg–Marquardt (LM) and Bayesian Regularization (BR). A database with 177 mixes selected from 15 studies incorporating RCA were selected, with the aim of having an underlying set of data heterogeneous enough to demonstrate the efficiency of the proposed approach, even when data are heterogeneous and noisy, which is the main finding of this work.