EuPtSi crystallizes in the cubic chiral structure (P2 1 3, No.198), which is the same as the noncentrosymmetric space group of MnSi with the skyrmion structure. The first-order antiferromagnetic transition occurs at T N = 4.0 K, and EuPtSi is in the helical magnetic state with the propagation vector q = (0.2, 0.3, 0) at low temperatures. We found the skyrmion structure in a closed H-T phase or the so-called "A-phase" for H ∥ [111], together with a new skyrmion-related phase named the "Bphase" for H ∥ [001]. It is characteristic that the A-phase is clearly observed in the magnetization, Hall resistivity, as-susceptibility, magnetostriction, and magnetoresistance. This is due to a small size of the skyrmion, 18 Å, in other words, a large number of the skyrmion density. The A-phase is thus anisotropic, not observed for H ∥ [110]. We also clarified the split Fermi surface properties based on the chiral nature of the crystal structure from the de Haas-van Alphen experiment and energy band calculation. Furthermore, we present the magnetic properties of EuPtGe with T N ≃ 3 K.