<p>In this paper, a new finite-volume multi-resolution weighted essentially non-oscillatory (MR-WENO) scheme is developed on mixed-element unstructured meshes. The reconstruction process is simplified to avoid the loss of the accuracy by using the polynomial on each stencil instead of their linear combinations in defining the smoothness indicator. Therefore, the modified MR-WENO scheme could obtain the optimal order of the accuracy in smooth regions with arbitrary positive linear weights. Moreover, two selection methods of the stencils are given based on edge neighbors and vertex neighbors, respectively; it is found that the vertex-based selection method performs well due to the compactness. Several numerical examples are given to illustrate that the new MR-WENO scheme has good performance on mixed-element meshes.</p>