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We investigate the ν-process in an energetic Type Ic supernova (SN Ic) and the 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 not only through spallation reactions as discussed in Nakamura & Shigeyama but also the ν-process. The ν-process is considered to occur in core-collapse supernovae and previous studies were limited to SNe II. Although the progenitor star of an SN Ic does not posses an He envelope so that ⁷Li production via the ν-process is unlikely, ¹¹B can be produced in the C-rich layers. We demonstrate a hydrodynamic simulation of a SN Ic explosion and estimate the amounts of the light elements produced via the ν-process for the first time, and also the subsequent spallation reactions between the outermost layers of the compact SN Ic progenitor and the ambient medium. We find that the ν-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 µ and τ 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.