Biodegradable electronic devices are presently in command in various sectors mainly in the health care system. The present work comprehends the dielectric properties of biodegradable composites made from biodegradable polymer poly (lactic) acid (PLA) and natural fiber of luffa cylindrical (LC) fabricated using micro compounding and injection molding. LC fibers are agricultural waste, rich in cellulose.LC fibers were exposed to a 6 MeV electron beam of doses 0.5Gy, 1.0Gy, 2.0Gy, 4.0Gy, and 10.0 Gy generated from a medical linear accelerator(LINAC) in presence of air. Such low doses are normally used for the treatment of cancer patients and not for modifying polymers where doses in the range of 20-200KGy are used. The effect of such low irradiation dose on fiber and study if any significant changes taking place is the innovative aspect of the present work. The effects of irradiation dose on dielectric constant and ac conductivity were investigated at different temperatures 260C, 40oC, 60oC, and 80oC while keeping the frequency constant. The increase in dielectric constant from 57 in virgin PLA at 260C,500Hz to a maximum of 84 in the composite sample due to reinforcement of low dose irradiated LC fibers recording a 49% increase is an important result of the investigation.