When the data-driven transient stability assessment model is used to judge the stability of power system, there can be an increase in the false positive rate of unstable samples. This is due to the imbalance between stable samples and unstable samples. Also the cost of misjudgment of unstable samples is much higher. An AC-LSTM transient stability assessment model with a cost-sensitive mechanism is proposed. By improving the Adaboost algorithm and introducing a cost-sensitive function to update the sample weights, the influence of minority samples on the overall classification accuracy is eliminated to minimize the false positive rate of unstable samples. In addition, the improved AdaBoost algorithm is integrated with long short-term memory (LSTM) to improve the comprehensive performance of the classifier. The simulation results on the IEEE39-bus and IEEE140-bus systems show that the model proposed has better adaptability and generalization ability than others, and the comprehensive evaluation performance is improved. In addition, the anti-noise ability is also better than other models. This work is supported by the National Natural Science Foundation of China (No. 61973072).