The noncentrosymmetric superconductor CaPtAs with time-reversal symmetry breaking in its superconducting state was previously proposed to host nodal superconductivity. Here, by employing ultralow-temperature thermal conductivity measurement on CaPtAs single crystal, we study its superconducting gap structure. A negligible residual linear term of thermal conductivity (κ 0/T) in zero magnetic field and the field dependence of κ 0/T indicate that CaPtAs has multiple superconducting gaps with a dominant s-wave component. This is consistent with recent nuclear quadrupole resonance measurements on CaPtAs. Our work puts a strong constraint on the theories to describe the superconducting pairing symmetry of CaPtAs.