The thick MgB2 films have been successfully grown on the Cu substrate by the technique of hybrid physical-chemical vapor deposition (HPCVD). The films are about 2 ~ 3 μm and quite dense. They possess the Tc (onset), as high as 37-38 K, and sharp transition ~ 0.8 K. X-ray diffraction (XRD) indicates their polycrystalline character. The upper critical field at T=0K, HC2(0), is extrapolated as 15.3T. The controlled growth of MgB2 film on Cu substrate opens a new route in the preparation of MgB2 tape materials.