A study of terahertz waves was made for the nondestructive evaluation of FRP (Fiber reinforced plastics) composite materials. The terahertz systems were consisted of time domain spectroscopy (TDS) and continuous wave (CW). The composite materials investigated include both non-conducting polymeric composites and conducting carbon fiber composites. Terahertz signals in the TDS mode resembles that of ultrasound; however, unlike ultrasound, a terahertz pulse was not able to detect a material with conductivity. The CFRP (Carbon fiber reinforced plastics) laminates were utilized for confirming the experimentation in the terahertz NDE. In carbon composites the penetration of terahertz waves is quite limited and the detection of flaws is strongly affected by the angle between the electric field direction of the terahertz waves and the intervening fiber directions. A refractive index (n) was defined as one of mechanical properties; so a method was obtained in order solve the "n" in the material with non-conductivity. The usefulness and limitations of terahertz radiation are investigated for the NDE of FRP composites.