Peeling compliant nano-films from supporting substrates is crucial in the mechanical exfoliation and transfer processes. However, the peeling behavior, especially concerning the peeling stiffness and peak peeling force, exhibits intricate interplay with the geometric and material properties of nano-films, as well as interfacial interactions, which have yet to be fully elucidated. In this work, both classical molecular dynamics (MD) simulations and continuum analysis are adopted to investigate the entire peeling process of compliant nano-films from a planar rigid substrate. Considering the atomic structure and van der Waals (vdW) interactions at the interface, we establish a continuum mechanics model to describe the entire peeling process, encompassing the initial, transitional, steady-state, and unstable peel-off stages. The theoretical predictions are reasonably consistent with the results obtained by MD simulations. The effects of film length and interface toughness on the peeling process, the peeling stiffness and peak peeling force, are thoroughly investigated, and a phase diagram for the peeling deformation modes is quantitatively constructed. Finally, dimensional analysis yields scaling relations for the peak peeling force in terms of the length and bending stiffness of compliant nano-films, as well as the governing parameters for interfacial vdW interactions. These results contribute to a better understanding of the peeling mechanics of various two-dimensional nano-films (e.g., graphene, hexagonal boron nitride, and molybdenum disulfide) adhered to substrates.