Proposing a microscopic model we have investigated the multiferroic properties of Sm2BaCuO5. The heat capacity shows two peaks at the antiferromagnetic transitions temperatures TN1∼ 5 K and TN2∼ 23 K. For the appearing of the extraordinary polarization ΔP in Sm2BaCuO5 we have considered the single-ion magnetostriction mechanism. ΔP is zero without magnetic field. An external magnetic field h induces an electric polarization ΔP below TN2 which varies linearly with h showing a linear magnetoelectric effect. Below TN1ΔP decreases due to ordering of the Sm-sublattice. There are some discrepancies in the experimental data for ΔP(T,h) which we will try to clarify. In addition, the temperature and magnetic field dependence of the dielectric constant is discussed. The observed maximum value of the peak at TN2 shifts to smaller temperature values and increases with increasing external magnetic field.