The absolute fluxes of the cosmic-ray antiproton are measured at solar minimum in the energy range 0.2 to 3.2 GeV, based on 460 antiprotons unambiguously detected by BESS spectrometer during its '95 and '97 balloon flights from Lynn Lake, Canada. In the resultant antiproton spectrum we have detected a clear peak around 2 GeV and measured its flux to 10 % accuracy. The position and the absolute flux of the peak agree with the prediction of the Standard Leaky Box model for the "secondary" antiprotons. At low energies below 1 GeV, we observe an excess antiproton flux over the simple Standard Leaky Box prediction. This might indicate that the propagation mechanism needs to be modified, or might suggest a contribution of low-energy antiproton component from novel sources such as evaporating primordial black holes or the annihilating neutralino dark matter. Data from '98 and future flights are expected to help us to clarify the situation.