We investigate the neutrino-process in an energetic Type Ic supernova (SN Ic) and resultant productions of the light elements including boron and its stable isotopes. SN Ic is a very unique boron source because it can produce boron through not only spallation reactions as discussed in Nakamura & Shigeyama (2004) but also the neutrino-process. The neutrino-process is considered to occur in core-collapse supernovae and previous studies were limited to Type II supernovae (SNe II). Although the progenitor star of an SN Ic does not posses a He envelope so that 7Li production via the neutrino-process is unlikely, 11B can be produced in the C-rich layers. We demonstrate a hydrodynamic simulation of SN Ic explosion and estimate the amounts of the light elements produced via the neutrino-process for the first time, and also the subsequent spallation reactions between the outermost layers of compact SN Ic progenitor and the ambient medium. We find that the neutrino-process in the current SN Ic model produces a significant amount of 11B, which is diluted by 10B from spallation reactions to get closer to B isotopic ratios observed in meteorites. We also confirm that high-temperature mu- and tau-neutrinos and their anti-neutrinos, reasonably suggested from the compact structure of SN Ic progenitors, enhance the light element production through the neutral-current reactions, which may imply an important role of SNe Ic in the Galactic chemical evolution.