Two-band Ginzburg-Landau (GL) theory is adopted to analyze the surface critical field Hc3 of Lu2Fe3Si5 . When the surface of a superconductor coincides with any of crystallographic planes and is parallel to the external magnetic field H, the ratio Hc3/Hc2 (where Hc2 is the upper critical field of Lu2Fe3Si5) is strongly dependent on temperature. When the surface of a superconductor coincides with the bc plane and is parallel to H, the ratio depends not only on temperature, but also on the angle between the c axis and H. However, the ratio is constant for single-band superconductors.