Metallic manganese nitrides Mn3AN (A=Zn, Ga, etc) are well known for their large magnetovolume effect (MVE), a discontinuous volume expansion at the magnetic transition. However, MVE is exceptionally absent in Mn3CuN. We found that MVE is induced by a small amount of Ge in the Cu site. This seems to coincide with recovery of the cubic structure. By further Ge doping, the volume expansion becomes gradual (ΔT~100 K) and large negative thermal expansion (NTE) is exhibited around room temperature [α=-12×10-6 K-1 (α: coefficient of linear thermal expansion) for Mn3(Cu0.5Ge0.5)N]. Such a large, isotropic and non-hysteretic NTE is desirable for practical applications.