As a perfect complement to conventional NMR that aims for chemical structure elucidation, Laplace NMR constitutes a powerful technique to study spin relaxation and diffusion, revealing information on molecular motions and spin interactions. Different from conventional NMR adopting Fourier transform to deal with the acquired data, Laplace NMR relies on specially designed signal processing and reconstruction algorithms resembling the inverse Laplace transform, and it generally faces severe challenges in cases where high spectral resolution and high spectral dimensionality are required. Herein, based on the tensor technique for high-dimensional problems and the sparsity assumption, we propose a general method for high-resolution reconstruction of multidimensional Laplace NMR data. We show that the proposed method can reconstruct multidimensional Laplace NMR spectra in a high-resolution manner for exponentially decaying relaxation and diffusion data acquired by commercial NMR instruments. Therefore, it would broaden the scope of multidimensional Laplace NMR applications.