Controllable story generation has been a hot topic in the field of natural language processing in recent years. Current research can effectively integrate text features and event features through the cross-attention mechanism. However, it lacks the efficient application of commonsense knowledge and still adopts the method of post-training on public commonsense knowledge corpora. Although this can improve the performance of the model to a certain extent, there is still much room for improvement in terms of adaptability. To solve this problem, a controllable story generation model with Adaptive Knowledge Enhancement (AKE) is proposed. The commonsense knowledge construction module in it can adaptively construct a matching commonsense knowledge corpus according to the training dataset during fine-tuning to ensure that more relevant additional information is provided for the model. In addition, a multi-task learning component trained with an auxiliary function is added to the model to ensure that it can learn more discriminative feature representations, thereby improving the generalization ability of the model. The experimental results show that AKE significantly outperforms other baseline models in both automatic evaluation indicators and manual evaluation indicators, verifying the superiority of this model in utilizing commonsense knowledge.