A detailed numerical investigation of combustion of unsupported and fiber supported n-heptane droplets in reduced gravity is presented. The primary focus is on the effects of support fibers on the droplet burning rates and flame structure. A 21-step n-heptane reaction mechanism consisting of 20 species is employed to model the combustion chemistry. The volume-of-fluid (VOF) method is employed to capture the liquid-gas interface while allowing for time-dependent two-phase multidimensional flows. Computed burning rates and flame stand-off ratios are compared with the experimental results of Jackson. Predicted flame structures are also validated with the experimental results of Mikami. The present computational results agree well with the experimental results. The results indicate that the support fibers can have significant impact on droplet burning rates and flame structure.