MgSiO_3-perovskite (MgPv) plays a crucial role in the Earth's lower mantle. This study combines deep-learning potential (DP) with density functional theory (DFT) to investigate the structural and elastic properties of MgPv under lower mantle conditions. To simulate complex systems, we developed a series of potentials capable of faithfully reproducing DFT calculations using different functionals, such as LDA, PBE, PBEsol, and SCAN meta-GGA functionals. The obtained predictions exhibit remarkable reliability and consistency, closely resembling experimental measurements. Our results highlight the superior performance of the DP-SCAN and DP-LDA in accurately predicting high-temperature equations of states and elastic properties. This hybrid computational approach offers a solution to the accuracy-efficiency dilemma in obtaining precise elastic properties at high pressure and temperature conditions for minerals like MgPv, which opens a new way to study the Earth's interior state and related processes.