The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC decompositions being the most prominent ones. Inspired by the latter, in this work we propose a multi-resolution low-rank tensor decomposition to describe (approximate) a tensor in a hierarchical fashion. The central idea of the decomposition is to recast the tensor into \emph{multiple} lower-dimensional tensors to exploit the structure at different levels of resolution. The method is first explained, an alternating least squares algorithm is discussed, and preliminary simulations illustrating the potential practical relevance are provided.