The evaporation behaviors of droplet containing nanoparticles play an important role in nanofluid combustion, spray drying, and so on. The average evaporation rate of a nanofluid droplet will decrease sharply at the end stage of droplet evaporation because the aggregation of nanoparticles on the surface of the droplet results in a shell. To illustrate the microscopic mechanism for the variation of the average evaporation rate and surface tension caused by the copper nanoparticles on the surface of the water droplet, numerical simulations based on the Brownian dynamics are conducted to study the effects of nanoparticle behaviors on the average evaporation rate and surface tension for various initial volume fractions and various distributions of nanoparticles. The results show us that the nanoparticles' distribution and the initial volume fraction of nanoparticles will greatly affect the average evaporation rate of the nanofluid droplet. Therefore, a D-h law can be expected due to the effects of added copper nanoparticles on the evaporation behavior where h will vary with the initial volume fraction and distribution of nanoparticles. Comparisons to the published results indicate that the exponent h = 2.0 for pure liquid, h < 2.0 when lyophilic nanoparticles are added, and h > 2.0 when lyophobic nanoparticles are added. In general, the most important factors to affect the evaporation rate are the volume fraction, distribution, and lyophilic nature of nanoparticles.