Based on the dynamics theory, the lower limit method of plastic limit analysis, the block element discrete technique and the mathematical programming theory, a lower limit method of time history analysis for the seismic dynamic stability of rock slopes is proposed in this paper. With this method, block unit is used to discrete a rock slope, and then seismic time history acceleration of its centroid is calculated using the pseudo dynamic principle. Finally, a linear mathematical programming model of seismic dynamic stability is established according to the balance equation, the yield condition and force boundary conditions of the rock slope. The mathematical programming algorithm is adopted to solve the model, and the variation of safety coefficient of rock slope stability under the action of earthquakes over time is obtained. Compared with the pseudo static method, which can only produce single value of slope safety coefficient, this method can provide both the time history curve and internal force time history curve of slope safety coefficient. This method has clear definition, is theoretically sound with high calculation accuracy and efficiency. It can be applied to the calculation of dynamic stability of rock slopes, providing reference for seismic design of rock slopes.