The effects of a magnetic field and pressure on the Kondo-like behavior in the valence-fluctuating antiferromagnetic compound EuPt2Si2 were studied using single-crystalline samples. The logarithmic temperature dependence of the electrical resistivity, ρ(T) ∞ -ln T, which is reminiscent of the Kondo effect, is robust against the application of a magnetic field. On the other hand, the temperature dependences of ρ(T) and thermoelectric power S(T) change markedly under pressure. In addition, the antiferromagnetically ordered temperature TN1 = 21K at ambient pressure decreases gradually and reaches zero at approximately P = 4 GPa. From the comparison of the magnetic properties of EuPt2Si2 with those of EuCu2(Ge0.4Si0.6)2, the observed anomalous features for EuPt2Si2 at low temperatures are inferred to be due to a valence fluctuation and=or a valence change of the Eu ions at low temperatures.