We report new ab initio dipole moment surfaces (DMS) of the electronic ground state of the H2S molecule. The two components of the dipole moment function have been evaluated using the coupled-cluster single and double excitations augmented by a perturbative contribution from connected tripled excitation (CCSD[T]) ab initio method. The rovibrational line intensities calculated with these ab initio DMS are in good agreement with the experimental data for fundamental nu (1), nu (2), and nu (3) bands. Our calculations reproduce the observed anomalies in the intensity distributions of rovibrational bands of H2S unlike the previous ab initio calculations. Since the DMS are very flat near the equilibrium geometry, the fundamental nu (1) and (3) bands are abnormally weak which makes the first principle intensity calculation a challenging problem.