With the advent of the Internet of Things era, people's demand for higher bandwidth and faster speed is increasing. The introduction of the terahertz frequency band provides a new solution to this problem. Terahertz signals bear the characteristics of strong penetrating power, good penetrability to non-metallic materials, and high resolution, and show great potential in the fields of communication and imaging. Based on the principle of photon assistance, a terahertz transmission system that uses photon heterodyne beat frequency to generate terahertz signals at two frequencies of 386.2 GHz and 438.4 GHz is built. And the penetration of terahertz signals is measured under the obstruction of four common plastic materials: poly4-methylpentene(TPX), polyethylene(PE), polypropylene(PP) and polymethyl methacrylate(PMMA). The attenuation characteristics of these materials in indoor environments are obtained, and the experimental results are fitted with Beer's absorption law. From the experimental results, it is found that the attenuation of terahertz signals by 5 mm thick PP board and PE board is below 1 dB, and the blocking effect of thin PP board and PE board on terahertz signals at 386.2 GHz and 438.4 GHz is very weak; terahertz signals in the frequency band selected for the experiment can hardly penetrate the 15 mm thick PMMA plate. The exploration and research on the transmission attenuation characteristics of terahertz signals in plastic materials has reference value for the selection of suitable antenna materials in millimeter-wave communication systems, and plays an important guiding role in practical applications.