Based on the theory of probability and mathematical statistics and on the results of nearly 2000 cases of elasto-plastic stability analysis for single-layer reticulated shells, a new simulation method of initial geometric imperfection distribution, N-order eigenmode imperfection method, is developed. The elasto-plastic stability analyses of four types of commonly used single-layer reticulated domes were conducted with the random imperfection mode method, the eigenmode imperfection method and the N-order eigenmode imperfection method, respectively, by means of ANSYS. The results show that, though the random imperfection mode method can simulate the initial geometric imperfection distribution realistically, the calculation cost of this method is too large to popularize in design practice. Adopting the first order eigenmode to simulate the distribution of initial geometric imperfection may fail to derive the most unfavorable buckling load. The reliability of buckling load obtained from the eigenmode imperfection method cannot be guaranteed effectively. The N-order eigenmode imperfection method can evaluate the influence of initial geometric imperfection on structural stability reasonably, and capture the buckling load satisfying the requirement of the ‘3σ’ principle with less calculation. This method is a convenient and efficient way for designers to estimate stability performance of single-layer reticulated shells accurately and safely.