BESS (Balloon-borne Experiment with a Superconducting Spectrometer) had its first circumpolar flight from Williams Field near McMurdo Station, Antarctica from Dec. 13 to 21, 2004. We have analyzed proton fluxes for this flight to study short-term variations in their intensities. Throughout a balloon flight, altitude varies, and, as a result, the atmospheric overburden changes. Precise determination of primary particle fluxes at the top of Earth’s atmosphere, requires a detailed correction for the effects of atmosphere on the fluxes observed by the detector. We carried out a careful analysis of BESS-Polar I data by dividing the whole flight data set into intervals of 4 hours. Then primary proton fluxes were individually determined for each of these time intervals after applying individual atmospheric corrections for each of these 4-hour intervals. Our sub-1% precision measurements of BESS Polar-I proton relative fluxes exhibit short-term variations after all instrumental effects are removed. The time progression of proton flux has two main features; a rising flux at the beginning of the flight, followed by quasi-periodic variation. Although the Sun was primarily quiet, arrival of a high-speed solar wind stream, enhancement of the interplanetary magnetic field, and a high energy multiple eruption solar energetic particle event occurred around this flight. In addition, the BESS-Polar I flight commenced during the recovery phase of a Forbush decrease. We present BESS-Polar I proton flux progression as a function of energy between 0.1 - 100.0 GeV and suggest possible physical interpretations of the observed variations in relation with interplanetary structures in the near-Earth space.