Abstract: A colored hydrogen - depleted graph was proposed to replace molecular graph so as to obtain good discrimination of the complex organic compounds by dyeing both the edges and the vertices. Furthermore, the topological index Xu based on the adjacency matrix A and distance matrix D was derived and further adapted to multiple bonds, heteroatom - containing compounds by using the related ratio of bond length to C-C bond in place of the adjacent topological distance and the valence δi in place of the degree of vertex υi in this paper. The index was highly correlated with the heat capacity of alkalies, olefins, aromatics, sulfur- containing and oxygen - containing compounds, etc. The calculated values were in good agreement with experimental data. The absolute average deviations of CpL for 79 compounds and CpG for 70 compounds were 1.57% and 2.24% , respectively. The proposed Xu index promised to be a useful parameter in QSPR/ QSAR research.