Abstract: The statistical properties of vibrational energy levels in C6H6 are analyzed. The results show that they belong to a completely different type, of which the spectral rigidity is larger but the fractal dimensional function is smaller than both the Wigner law and Poisson law, and this new statistical property is called the low Poisson law. In fact, this special statistical property reflects the speciality in the structure of C6H6 in a way.