In order to predict the relative dynamic elastic modulus (RDEM), which is used to reflect the frost resistance of iron ore tailings concrete, the backpropagation neural network (BPNN) was used in this study. Here, one hidden layer was chosen in the structure of BPNN. It is well known that the number of neurons in the hidden layer is the key of BPNN; hence, checking the features of overfitting was chosen in this paper to determine the number of neurons in the hidden layer. According to the actual conditions of freeze–thaw cycle test, a BPNN model of 2D input vector and 1D output vector was established. Thirty datasets from the test were used for training and test the proposed ANN. The results showed that the predicted values were in good agreement with the measured ones, and the correlation coefficient between them reached 0.9505. It showed that the BPNN, with the ability to solve nonlinear problems, had great advantages in predicting RDEM, and it can be used as reliable and simple forecasting tools for the prediction of frost resistance of iron ore tailings concrete.