Bidirectional privacy-preservation federated learning is crucial as both local gradients and the global model may leak privacy. However, only a few works attempt to achieve it, and they often face challenges such as excessive communication and computational overheads, or significant degradation of model accuracy, which hinders their practical applications. In this paper, we design an efficient and high-accuracy bidirectional privacy-preserving scheme for federated learning to complete secure model training and secure aggregation. To efficiently achieve bidirectional privacy, we design an efficient and accuracy-lossless model perturbation method on the server side (called $\mathbf{MP\_Server}$) that can be combined with local differential privacy (LDP) to prevent clients from accessing the model, while ensuring that the local gradients obtained on the server side satisfy LDP. Furthermore, to ensure model accuracy, we customize a distributed differential privacy mechanism on the client side (called $\mathbf{DDP\_Client}$). When combined with $\mathbf{MP\_Server}$, it ensures LDP of the local gradients, while ensuring that the aggregated result matches the accuracy of central differential privacy (CDP). Extensive experiments demonstrate that our scheme significantly outperforms state-of-the-art bidirectional privacy-preservation baselines (SOTAs) in terms of computational cost, model accuracy, and defense ability against privacy attacks. Particularly, given target accuracy, the training time of SOTAs is approximately $200$ times, or even over $1000$ times, longer than that of our scheme. When the privacy budget is set relatively small, our scheme incurs less than $6\%$ accuracy loss compared to the privacy-ignoring method, while SOTAs suffer up to $20\%$ accuracy loss. Experimental results also show that the defense capability of our scheme outperforms than SOTAs.