Low-temperature (T ) thermodynamic properties in magnetic fields (B) of the quasi-Kagome antiferromagnet CePdAl (T N ∼ 2.7 K) were studied by means of magnetization and specific-heat C(T, B) measurements. The unusual magnetic phase diagram, including three thermodynamic phases I-III, and crossover anomalies, has been obtained. In low-field phase I, the existence of the partial Kondo screening state on the one-third Ce sites is supported from the thermodynamic point of view: (i) an appearance of the paramagnetic moment with one-third of the full moment around 3 T, and (ii) an occurrence of the entropy release ∼0.3Rln2 around the observed crossover. On the other hand, a strong enhancement of C/T is found around the point, where T N (B) meets the boundary of phase III, indicating the possible presence of a tri-critical point. Furthermore, it is suggested that the three metamagnetic transitions at B mi (i =1,2,3) come from successive increments of the Ising-type magnetic moment along the c-axis. In high-field state above 20 T, the behavior of f electron can be rather described by the crystal-electric-field model.