In this paper, the technique of series solution to a class of initial value problems is developed and assessed by Taylors' series for an accurate simulation of two-dimensional nonlinear biological population model. To examine the accuracy and performance of the present solution technique whose derivation is based on Taylors' series expansion, three standard test problems are simulated. To show the efficiency and accuracy of the recent solution technique, the results of an approximate analytic solutions that we obtain are compared with Adomian decomposition method (ADM), variational iteration method (VIM), improved element-free Galerkin method (IEFGM) and the modified cubic B-Spline differential quadrature method (MCB-DQM). The proposed simulation technique is precise, efficient, and has agreeable convergence for solving two-dimensional biological population model.