Nonlinearity is an inherent property of geo-materials. Under this property condition， the potential sliding surface of a homogeneous slope based on the rotational failure mechanism is not a single log-spiral under the nonlinear failure criterion. Therefore， the geo-materials of the slope are assumed to obey the three-parameter nonlinear strength criterion， and the rotational failure mechanism of the homogeneous slope was constructed based on the upper bound theorem of limit analysis. The seismic load was introduced through a pseudo-static method， and the differential equations of the critical sliding surface and its corresponding stress distribution of homogeneous slope were obtained according to the mechanical equilibrium equations and the variational principle. And then the equations were solved by the Runge-Kutta method. According to the virtual power principle， the minimum critical height of the slope was optimized through Immune Algorithm （IA）. The accuracy and validity of the nonlinear upper bound variation analysis method were verified by comparing it with the results of finite element limit analysis （FELA）. On this basis， the effects of dimensionless strength parameters （T， A， n）， the horizontal seismic acceleration coefficient （kx）， and slope angle （β） on the slope stability factor Fn， potential sliding surface， and its stress distribution were analyzed. There is no need to assume the potential sliding surface of the slope， and this work enriches the nonlinear analysis theory of slope stability and provides theoretical support and useful reference for slope reinforcement design.