In this paper, the performance of feed-forward backpropagation (BP)—artificial neural network (ANN) was evaluated in predicting the construction project cost (CPC). The models include several factors involving the floor area (FA), number of floors (NF), structural material type of the building (MT), height of the building (HB), number of columns (NC), area of the concrete hollow blocks wall (CHB), volume of concrete (VC), weight of steel (WS), and contract duration (CD). The developed neural network model was evaluated based on several accuracy metrics such as correlation coefficient (R), mean squared error (MSE), mean absolute percentage error (MAPE), and Akaike Information Criterion (AIC). The simulation results showed that the governing model has an excellent R value of 0.99885 and a MAPE of 2.5826%. The comparison results between the ANN and multiple linear regression (MLR) suggest that the ANN model provided superior performance with MAPE which is 4.777 times better than that of the MLR model. Moreover, the lowest AIC value was observed in the 9–21-1 network structure suggesting that this is the governing network model for predicting the CPC. The sensitivity analysis (SA) using Garson’s Algorithm (GA) quantitatively determines the relative contribution (RC) of the input parameters (IP) to the construction project cost. The developed model could be utilized as a support instrument for minimizing the cost overruns and losses that may have been incurred in a construction project (CP).