• A support vector machine with pinball loss is developed for TSA. • Quantile parameter is conducted to improve the robustness of TSA. • Sequential minimal optimization is adopted to accelerate the computational efficiency of TSA. Recent studies show that support vector machine is a promising approach for predicting the transient stability of power systems. However, most of the existing support vector machine methods suffer from excessive training time and low robustness, resulting in inefficiency for implementation. In this paper, a novel TSA method using sequential minimal optimization based support vector machine with pinball loss is developed. In the proposed approach, the system operation indices and projected energy function indices are selected to form the initial TSA feature set. Then, a quantile parameter is introduced to reduce the impact of measurement error by controlling the positions of the boundary samples between stable and unstable classes. Finally, a sequential minimal optimization is applied to decompose the large quadratic programming problem into a series of small quadratic programming problems to accelerate the computational efficiency. The cross-validation and grid search methods are introduced to improve the classification stability and accuracy. The IEEE 50-machine test system and the China Southern Power Grid are used to evaluate the performance of the proposed TSA method. Simulation results demonstrate that the proposed TSA method has high accuracy, robustness, and computational efficiency in bulk power grids.