The real-time battery monitoring often involves two contradicting requirements, i.e., high accurate modeling and low computational time. The main contribution of this study is developing a reduced order model to accurately simulate a lead-acid battery without any simplification which can be used for real-time monitoring, optimization and control purposes. In this paper, the governing equations of lead-acid battery including conservation of charge in solid and liquid phases and conservation of species are solved simultaneously during discharge, rest and charge processes using an efficient reduced order model based on proper orthogonal decomposition (POD). A comprehensive description of numerical difficulties of lead-acid battery transport equations is also discussed both mathematically and graphically. Effect of different operating conditions such as applied current density and the dependency of open circuit potential to the acid concentration on dynamic behavior of lead-acid cell are investigated to show the capability of present method. Moreover, an extensive analysis of eigenvalues, spatial patterns and temporal trends of lead-acid battery model is presented to comprehensively determine the basic dynamic characteristics. The obtained numerical results show that not only the POD-based ROM of lead-acid battery significantly decreases the computational time (speed-up factor of 15) but also there is an excellent agreement with the results of computational fluid dynamics (CFD) models.