The effective dose equivalent, H (or the effective dose, E) to an individual is the primary limiting quantity in radiation protection. However, techniques for measuring H for neutrons have not been fully developed. In this regard a new tissue equivalent proportional counter (TEPC) based on a gas electron multiplier (GEM) for measuring H for neutrons was designed and constructed. The deposited energy distribution for two different neutron sources (a Cf-252 source and an AmBe source) was measured using the new TEPC. The measurements were performed using two different proportional gases: P-10 gas and a propane-based tissue equivalent gas at various pressures. A computer simulation of the new TEPC, based on the Monte Carlo method, was performed in order to obtain the pulse height distributions for the two neutron sources. The simulated results and the measured results were compared. Results show that the experimental results agree with the computational results within 20% of accuracy for both Cf-252 and AmBe neutron sources. A new model GEM-based TEPC was developed for use in obtaining H*(10), which provides an estimate for H. The study shows that the GEM-based TEPC can successfully estimate H*(10). With these results and some refinements, this GEM-based TEPC can directly be used as a neutron rem meter.