We report resistivity and magnetization of single crystal MgB2, focusing on the broadening of superconducting (SC) transition in magnetic fields. In-plane and out-of-plane resistivity indicate that the broadening of superconducting transition is independent of Lorentz force and that it is merely dependent on the magnetic field direction. In magnetization, diamagnetic signal begins to appear at almost the same temperature as the onset temperature of resistivity transition. These results suggest that the broadening is attributed not to the surface superconductivity but to the superconducting fluctuation or the vortex-liquid picture, owing to the short coherence length and the high transition temperature of MgB2.