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As-grown superconducting MgB2 thin films were prepared on Al2O3  single crystals by electron beam deposition technique by changing the substrate temperature, the flux rate ratio of Mg/B and the basal pressure before the deposition starting. Higher Mg deposition rate and lower basal pressure gave a lower normal state resistivity of the MgB2 thin films and gave a higher critical temperature. Magnetic hysteresis of the MgB2 film prepared under lower basal pressure was smaller than that of the film prepared under higher basal pressure. Although the critical temperature of the MgB2 film prepared under higher basal pressure became lower, the critical current density was enhanced. Higher basal pressure introduced some pinning centers in to MgB2 films. These results suggest that precision control of the atmosphere during the MgB2 deposition is very important for obtaining the high critical current density.