In this paper we report experimental and theoretical results on total inelastic cross-sections for NH3 molecules colliding with H-2 at room temperature. The use of time resolved infrared-infrared double resonance allows one to follow the population relaxation for different energy levels of NH3. A CO2 pulsed pump laser tuned to a line in the nu2 band of NH3 induces a transient transfer of population and the return to equilibrium is probed with a c.w. diode laser turned to lines in the nu4 band of NH3. The time evolution of the probe absorption for different pressures of the two gases is then related to the inelastic cross-sections of the states involved. The so-determined cross-sections for the (j = 5 k = 4 epsilon = + 1) and (j = 1, k = 1, epsilon = - 1) states of NH3 are respectively 27 angstrom2 and 31 angstrom. We have also calculated inelastic cross-sections using a semi-classical model and an ab initio potential energy surface for different values of ( j, k, epsilon) (i.e. j = 1,2,3, k = 1,2,3 and epsilon = +/- 1) and of j2 (total angular momentum of H-2). These calculated values are in agreement with the experimental results.