In this paper, specific features of Sm magnetism in an intermetallic compound have been studied. For this purpose, a high-quality single crystal of SmPd2Al3 was grown and subjected to detailed measurements of specific heat, magnetization, ac susceptibility, and electrical resistivity with respect to temperature and a magnetic field applied along the principal crystallographic directions. SmPd2Al3 magnetism was found to be strongly anisotropic with the easy-magnetization direction along the c axis where the main magnetic features are concentrated. The a-axis response remains weak, paramagneticlike, even in the magnetically ordered state. Ferromagnetism with TC=12.4 K has been indicated by all the measured physical properties. At lower temperatures, three successive order-order phase transitions have been observed on the temperature dependence of the specific heat as three anomalies: at 3.4, 3.9, and 4.4 K, respectively. The low-temperature magnetization data can be understood within a scenario that considers the antiferromagnetic ground state as being gradually destroyed through a series of four metamagnetic transitions at 0.03, 0.35, 0.5, and 0.75 T, as detected in the 1.8 K magnetization data. The experimental data are discussed together with the results of electronic-structure and crystal-field calculations from first principles, which were performed as an important part of the study for comprehension and explanation of the observed behavior of the SmPd2Al3 compound.