Hybrid organic-inorganic perovskite materials are promising materials for photovoltaic and optoelectronic applications. Nevertheless, the construction of a computationally efficient potential model for atomistic simulations of perovskite with high fidelity to ab initio calculations is not a trivial task given the chemically complex nature of perovskite in terms of its chemical components and interatomic interactions. In the present study, we demonstrate that artificial neural network (ANN) models can be employed for efficient and accurate potential energy evaluation of MAPbI perovskite materials. The ANN models were trained using training sets composed of thousands of atomic images of tetragonal MAPbI crystals, with their respective energies and atomic forces obtained from ab initio calculations. The trained ANN models were validated by predicting the lattice parameters and energies/atomic forces of cubic MAPbI perovskite and had excellent agreement with ab initio calculations. The phonon modes could also be extracted using the trained ANN model with good agreement with ab initio calculations, provided that the atomic forces were incorporated into the training processes. Finally, we demonstrate that for a given system size, the trained ANN model offers 10 to 10 faster time consumption per energy evaluation relative to ab initio calculations using Vienna Ab initio Simulation Package, demonstrating the potential of the ANN model for exhaustively sampling the configuration spaces of chemically complex materials for predictions of thermodynamic properties and phase stabilities.