Recently, continuous transform-based tensor representation has emerged as a promising tool for multi-dimensional data recovery. However, the existing continuous transforms are essentially single-layer linear mappings, which limits their ability to capture the complex relationships inherent in multi-dimensional data. To overcome this limitation, we propose a Hierarchical Nonlinear Continuous Transform-based Tensor Representation (HiNCoT) for multi-dimensional data recovery. By leveraging the hierarchical nonlinear continuous transform, HiNCoT constructs the recovered tensor from a latent tensor, which is generated by the deep representation module with a low-rank core tensor as input. Compared with the existing continuous transform-based methods, HiNCoT can more effectively capture the complex nonlinear relationships inherent in multi-dimensional data along the third dimension. To evaluate the effectiveness of the proposed HiNCoT, we suggest an HiNCoT-based multi-dimensional data recovery model. Extensive experiments on diverse degeneration scenarios demonstrate the superiority of our hierarchical nonlinear transform-based method over existing single-layer linear transform-based methods.