Abstract: The existence of the global minimizers of the Ginzburg-Landau functional for an anisotropic superconducting sample in a magnetic field h_ex below the first critical field H_C_1 is proved. It is shown that there exists a vortex-less solution coincide with the solution found by the authors in a related paper, and that the density of the vortices is relevant to the applied field as H_c_1h_exH_c_2.