We propose a mesoscopic approach for investigating steady/transient nanoscale evaporation heat transfer characteristics, whose kinetic nature makes it an ideal tool to model the evaporation kinetics at the liquid-vapor interface and the microscopic wall-fluid interactions. Simulation of the evaporation of a flat nanoscale thin liquid film demonstrates its capability of resolving kinetically limited evaporation and liquid film adsorption. For the simulation of an evaporating meniscus in a nanochannel, our proposed mesoscopic approach considers the conservation of mass, momentum and energy of both liquid and vapor phases, thereby naturally incorporating both the multi-dimensional heat transfer effect and vapor transport resistance in nano-confined space. We demonstrate that solid-fluid interaction plays dominant roles on the interfacial transport during nanoscale evaporation, and vapor transport resistance has nonnegligible influences on the evaporation heat/mass transport in nano-confined spaces. By handling statistical behavior of molecule ensembles, this mesoscopic approach not only preserves microscopic physics but also has high computational efficiencies, enabling the simulation of space and time domains on the practical application level. This work paves the way for quantitative investigations of steady/transient nanoscale evaporation heat transfer characteristics using mesoscopic approach.