The electrical resistivity, thermal properties, pressure effect on the Néel temperature and compressibility of Mn3+xRh1-x (x = 0.0, 0.12, 0.20 and 0.32) alloys have been investigated in order to discuss the magnetovolume effects in both ordered and disordered states. The electronic specific heat coefficient γexp of the Mn3Rh ordered alloy is slightly smaller than that of the disordered one, qualitatively consistent with the theoretical calculations. A negative magnetovolume effect is observed below the Néel temperature TN in both the ordered and disordered alloys. Furthermore, the magnetic contribution to the thermal expansion is significant even in the paramagnetic region. That is, the thermal expansion coefficient α in the paramagnetic region shows a large value of about 30 × 10-6 K-1, because of a significant contribution from spin fluctuations. For the Mn3Rh ordered alloy, the pressure shift of the Néel temperature, dTN/dP, is estimated to be about 7.0 K GPa-1. The temperature dependence of α exhibits a pronounced positive peak at TN in accordance with the positive pressure dependence of TN. A large compressibility of 1.4 × 10-2 GPa-1 has been obtained from the change in the lattice constant under pressure.