Current harmonic voltage or current based assessment index of harmonic contribution is sensitive to harmonic impedance of utility side and customer side and it's available only for special cases. In order to solve this problem, this paper, which bases itself on the fact that the essence of power system is electric energy conversion and transmission, studies the physical mechanism of power flow when voltage and current are distorted and uses Poynting vector to compare different definition of distortion power. Then a nonfundamental apparent power based index is proposed to assess harmonic contribution of multi-harmonic sources and detail studies on calculating algorithm are explored with the help of current vector method. The proposed index is verified by theoretical simulation and laboratory test, and the assessment results of harmonic contribution by the proposed index are compared with those by conventional index with voltage and current. Comparison results show that the proposed index in this paper is rational and feasible. This work is supported by the State Grid Corporation of China (No. SGRI-DL-71-15-006).