A neutron-TPC (nTPC) is being developed for use as a fast neutron spectrometer in the fields of nuclear physics, nuclear reactor operation monitoring, and thermo-nuclear fusion plasma diagnostics. An nTPC prototype based on a GEM-TPC (Time Projection Chamber with Gas Electron Multiplier amplification) has been assembled and tested using argon-hydrocarbon mixture as the working gas. By measuring the energy deposition of the recoil proton in the sensitive volume and the angle of the proton track, the incident neutron energy can be deduced. A Monte Carlo simulation was carried out to analyze the parameters affecting the energy resolution of the nTPC, and gave an optimized resolution under ideal conditions. An alpha particle experiment was performed to verify its feasibility, and to characterize its performance, including energy resolution and spatial resolution. Based on the experimental measurement and analysis, the energy resolution (FWHM) of the nTPC prototype is predicted to be better than 3.2% for 5 MeV incident neutrons, meeting the performance requirement (FWHM<5%) for the nTPC prototype.