We report the synthesis of BaPt2As2 single crystals and the discovery of superconductivity and a structural phase transition in this compound by measuring the electrical resistivity, magnetic susceptibility and specific heat as well as the x-ray diffraction at low temperatures. BaPt2As2 crystallizes in the CaBe2Ge2-type tetragonal structure (P4/nmm) at room temperature and undergoes a first-order structural transition at TS ≃ 275 K, which is likely to be associated with a charge-density-wave (CDW) instability. BCS-like superconductivity with two subsequent transitions Tc1 ≃ 1.67 K and Tc2 ≃ 1.33 K is observed. Our results demonstrate that BaPt2As2 may serve as a new system for studying the interplay of superconductivity and the CDW order.