We report on in situ high-pressure studies up to 1.0 GPa on the MgB2 superconductor which was high-pressure synthesized. The as-prepared sample is of high quality in terms of sharp superconducting transition (T c) at 39 K from the magnetic measurements. The in situ high-pressure measurements were carried out using a Be-Cu piston-cylinder-type instrument with mixed oil as the pressure transmitting medium which warrants a quasi-hydrostatic pressure environment at low temperature. The superconducting transitions were measured using the electrical conductance method. It is found that T c increases by more than 1 K with pressure in the low-pressure range, before the T c value decreases with the further increase of the pressure.