With the rapid development of recommendation models and device computing power, device-based recommendation has become an important research area due to its better real-time performance and privacy protection. Previously, Transformer-based sequential recommendation models have been widely applied in this field because they outperform Recurrent Neural Network (RNN)-based recommendation models in terms of performance. However, as the length of interaction sequences increases, Transformer-based models introduce significantly more space and computational overhead compared to RNN-based models, posing challenges for device-based recommendation. To balance real-time performance and high performance on devices, we propose Device-Cloud Collaborative Correction Framework for On-Device Recommendation (CoCorrRec). CoCorrRec uses a self-correction network (SCN) to correct parameters with extremely low time cost. By updating model parameters during testing based on the input token, it achieves performance comparable to current optimal but more complex Transformer-based models. Furthermore, to prevent SCN from overfitting, we design a global correction network (GCN) that processes hidden states uploaded from devices and provides a global correction solution. Extensive experiments on multiple datasets show that CoCorrRec outperforms existing Transformer-based and RNN-based device recommendation models in terms of performance, with fewer parameters and lower FLOPs, thereby achieving a balance between real-time performance and high efficiency. Code is available at https: //github.com/Yuzt-zju/CoCorrRec.