We study the temperature dependence of the upper critical field Hc2(T) for superconducting magnesium diboride, MgB2 in the vicinity of Tc using a two-band Ginzburg-Landau (G-L) theory. The temperature dependence of Hc2(T) near Tc exhibits a positive curvature. In addition, the calculated temperature dependence and its higher-order derivatives are also shown to be in good agreement with the experimental data. In analogy with the multi-band character of the Eliashberg microscopic theory, the positive curvature of Hc2(T) is described reasonably by solving the two-band G-L theory.

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