Tensor-valued data, increasingly common in distributed big data applications like autonomous driving and smart healthcare, poses unique challenges for privacy protection due to its multidimensional structure and the risk of losing critical structural information. Traditional local differential privacy methods, designed for scalars and matrices, are insufficient for tensors, as they fail to preserve essential relationships among tensor elements. We introduce TLDP, a novel LDP algorithm for Tensors, which employs a randomized response mechanism to perturb tensor components while maintaining structural integrity. To strike a better balance between utility and privacy, we incorporate a weight matrix that selectively protects sensitive regions. Both theoretical analysis and empirical findings from real-world datasets show that TLDP achieves superior utility while preserving privacy, making it a robust solution for high-dimensional tensor data.