The Lotka-Volterra predator-prey biological model is mainly studied in this paper by introducing the new population which has no ability to prey the other population to form a simple competition between predator and prey when the number of predators is excessive. Based on above condition, differential algebraic biological model is established according to the conservation. Then, the stability of biological model is discussed when the parameters change in a certain range by applying the stability analysis method and the related criteria of differential algebraic system. Finally, the model is the simulated numerically by considering the results of the analysis and using the Matlab software, and the simulation results show that the system has a limit cycle when the parameters vary a certain value, which proved that the complex nonlinear phenomena exist in the differential algebraic biological model.