Measurements of the density and isobaric specific heat capacity for HFO-1234ze(E) (trans-1,3,3,3-tetrafluoropropene)+HFC-32 mixtures were carried out using a metal-bellows calorimeter. Seventy-one densities and thirty-eight isobaric specific heat capacities were obtained in the range of temperatures from 310 to 350 K, pressures from 1.4 to 5.0 MPa, and densities from 724 to 1083 kg‧m^-3. The experimental uncertainties are estimated to be ±10 mK in temperature, ±2 kPa in pressure, ±0.001 mol‧mol^-1 in composition, ±0.2 % in density, ±5 % in isobaric specific heat capacity. On the basis of the present data, the bubble point pressure, the saturated liquid density, and the isobaric specific heat capacity of saturated liquid were also determined. The experimental results were compared with the values calculated from REFPROP.