Lithium-ion batteries (LIB) have been prevalently used as an energy storage system in numerous devices. Real-time, highly accurate numerical simulation of lithium batteries is a crucial prerequisite for many applications such as battery online state monitoring and controlling, optimization, and uncertainty quantification. The pseudo-two-dimensional (P2D) model is one of the most accurate models for LIB modeling, however, it suffers from the disadvantage of long simulation time which prevents its widespread applications. Numerical simulations indicate that the main time-consuming parts of the total execution time are allocated to solve the potential system of equations (40%) and the solid concentration equation (45%). In this paper, two new numerical schemes are proposed to solve the full-order P2D model both efficiently and accurately. First, a modified boundary condition treatment is introduced to solve the potential system of equations using the physical understanding of the charge conservation. Secondly, a third-order vertex-based finite-volume method is presented to solve the solid concentration equation. Execution time of these new schemes is studied in the galvanostatic discharge condition using various computational grids and C-rates. The results not only show a good agreement with the previous experimental data but also indicate a significant reduction in the execution time. (C) 2019 The Electrochemical Society.