Thermal run-away of lead acid batteries is one of the destruction modes of lead-acid battery. This phenomenon is a thermal-fluid dynamics instability problem that needs to be solved via direct numerical procedures. High-order simulation of lead-acid battery is the first step of direct numerical simulation (DNS) methods for research on thermal run-away phenomenon. In this study, due to simple geometry of lead-acid-cell, spectral methods which are very common in DNS simulation of thermal and fluid dynamics instability problems is implemented on lead-acid cell. A full cycle of discharge, rest and recharge process of a lead-acid cell is simulated by Chebyshev spectral collocation method combined with fourth order Runge-Kutta time integration. Due to complexities, the simulations are performed to find the possible numerical difficulties of this method as the first step. Two coarse and fine grids with Chebyshev polynomials of 8 and 12 order are selected to perform numerical simulations. Comparison of the error shows that the accuracy will be decreased up to 200 times just by adding two points to grid. Also numerical results show that this method is sufficiently able to predict the cell behavior in the high rates of cell current. The results indicate that spectral methods and Runge-Kutta time integrations are promising tool for direct numerical simulation of lead-acid batteries to study complex physical phenomena such as thermal run-away problem.