The MnCoGe alloy can crystallize in either the hexagonal Ni2In- or the orthorhombic TiNiSi-type of structure. In both phases MnCoGe behaves like a typical ferromagnet with a second-order magnetic phase transition. For MnCoGeBx with B on interstitial positions, we discover a giant magnetocaloric effect associated with a single first-order magnetostructural phase transition, which can be achieved by tuning the magnetic and structural transitions to coincide. The results obtained on the MnCoGe-type alloys may be extensible to other types of magnetic materials undergoing a first-order structural transformation and can open up some possibilities for searching magnetic refrigerants for room-temperature applications