The magnetic transition process in double-layer perovskite manganites is rather different from that in the counterpart compound with standard perovskite structure. In this paper, the magnetic phases below room temperature as well as the order of magnetic phase transition in terbium (Tb) doped La4/3Sr5/3Mn2O7 are studied by analyzing the magnetization curves, including thermal hysteresis, magnetic entropy change and its universal curve. The electrical conductivities with and without applied magnetic field are also discussed. Both the undoped and the doped samples (La1-xTbx)4/3Sr5/3Mn2O7 (x=0, 0.025) are prepared through the conventional solid-state reaction of mixed La2O3, Tb2O3, MnCO3 and SrCO3 whose purities are all higher than 99.9%. The mixture is calcined twice at 1000℃ for 12 h. Subsequently, the compactly compressed tablet of the calcined mixture is sintered in air at 1350℃ for 24 h. The data of X-ray diffraction show that the crystallographic structures of both samples are in the Sr3Ti2O7-type tetragonal phase with the space group I4/mmm. The refinement result indicates that the smaller radius of doped Tb3+ reduces all three lattice parameters as well as the c/a ratio, which is attributed to the preferential occupation of Tb3+ on the R site in rocksalt layer instead of the P site in perovskite layer. The temperature and field dependence of magnetization M(T, H), are recorded using the vibrating sample magnetometer of physical property measurement system (Quantum Design). Upon reducing the temperature, both samples exhibit two magnetic phase transitions from the paramagnetic phase at high temperature to the two-dimensional shortrange-ordered ferromagnetic state at the intermediate temperature, and finally the three-dimensional long-range-ordered antiferromagnetic state at low temperature. The zero-field-cooling and field-cooling curves display the characteristics of spin-glass behavior which may be due to the competition between B-site ferromagnetic and antiferromagnetic interactions associated with the randomly distributed A-site ions. The magnetic entropy changes of the samples are obtained through analyzing the magnetization data. The maximal magnetic entropy changes under 7 T magnetic field of the two samples are -4.60 J/(kgK) and -4.18 J/(kgK), respectively. The doped Tb ions reduce the transition temperatures, Tc2D and Tc3D, as well as the maximal value of magnetic entropy change, and increases the transition temperature range. The re-scaling curves of magnetic entropy change at different magnetic fields do not fall into a universal one, rather disperse in a wide interval, which suggests that the system undergoes a weak first-order transition at Tc3D. This conclusion is supported by the thermal hysteresis observed in the magnetization data. In addition, the electrical resistivity of the doped sample can be explained by using the small polaron model, which is different from three-dimensional variable-range hopping mechanism of undoped sample. On reducing temperature, the doped sample undergoes metal-insulator transition at temperature TP about 115 K, which is different from the undoped sample that shows the shoulder-shaped MI transition peaks. Under finite fields, the magnetoresistance value of intrinsic nature is about 56% near Tc3D.