In this paper we present experimental results obtained for CePdBi by means of specific heat, electrical resistivity, magnetization and x-ray photoemission spectroscopy (XPS) measurements as well as fully relativistic band structure calculations. CePdBi crystallizes in MgAgAs structure and exhibits a transition to a magnetically ordered state at TM ~/= 2 K, and a subsequent transition to a superconducting state at TC ~/= 1.3 K. The superconducting phase has a significant critical field of about 1.4 T. The x-ray diffraction, resistivity and magnetic susceptibility data show that CePdBi exhibits significant atomic disorder, which is a typical feature of Heusler alloys. It seems that the superconducting transition is caused by part of the disordered phase, which from the Meissner shielding can be estimated to constitute ~8% of the sample volume. Due to atomic disorder, CePdBi exhibits metamagnetic behavior below TM and spin-glass-like features just above TM. Band structure calculations confirm the magnetic ground state of the CePdBi system and the possibility of formation of a narrow pseudogap near the Fermi level, which can also be seen in resistivity data. The spin-orbit interaction strongly influences the band structure and the shape of the semiconducting gap.