Scanning SQUID microscope (SSM) is a powerful tool for observing small magnetic flux. It measures the z-component signal of flux density, but it is also available for observation of current distribution by inverting the Biot-Savart's law. We report the two-dimensional vector mapping of current distributions in high-T c superconducting YBa 2 Cu 3 O 7 - y (YBCO) thin films obtained by converting magnetic-field data measured by SSM. The current distribution contains those from both transport supercurrent and vortex current. The transport supercurrent is found to flow mainly along the edge of a stripline. The results are in good qualitative agreement with the calculated results based on simple London model. The YBCO films with an artificial grain boundary, i.e. Josephson boundary are also observed. The transport current seems to flows with avoiding the vortices, and an irregular vortex is observed at a point of grain boundary.