Generalized relativistic effective core potentials (GRECP) were used in the framework of the Fock-space relativistic coupled-cluster method to calculate the spectroscopic constants of HgH and HgH⁺ ground states as well as HgH low excited states. Some 21 electrons were treated explicitly in the molecule, of which 19 were correlated by relativistic coupled cluster (RCC). Basis set superposition errors were evaluated by counterpoise correction, and contributions of triple excitations of the external electrons were estimated in a reduced basis. The resulting spectroscopic constants of the HgH and HgH⁺ states show excellent agreement with experiment.