The superconductivity of a kagome superconductor CsV_{3}Sb_{5} is studied by scanning tunneling microscopy and spectroscopy at ultralow temperature with high resolution. Two kinds of superconducting gaps with multiple sets of coherent peaks and residual zero-energy density of states (DOS) are observed on both half-Cs and Sb surfaces, implying multiband superconductivity. In addition, in-gap states can be induced by magnetic impurities but not by nonmagnetic impurities, suggesting a sign-preserving or s-wave superconducting order parameter. Moreover, the interplay between charge density waves (CDW) and superconductivity differs on various bands, resulting in different density-of-states distributions. Our results suggest that the superconducting gap is likely isotropic on the sections of Fermi surface that play little roles in CDW, and the superconducting gaps on the sections of Fermi surface with anisotropic CDW gaps are likely anisotropic as well. The residual spectral weights at zero energy are attributed to the extremely small superconducting gap on the tiny oval Fermi pockets. Our study provides critical clues for further understanding the superconductivity and its relation to CDW in CsV_{3}Sb_{5}.