Micro-mechanism of granular materials is complicated for the discrete behaviour. Numerical method of DEM is applied to the study of micro-structure of binary packing of spherical particles in terms of size and distribution of coordination number under the influence of gravity force. Results show that the volume fraction influences the distributions of coordination number of single contact type and individual components. It features that increasing the volume fraction of small component increases the small-to-small and large-to-small contacts and decreases the small-to-large and large-to-large contacts. The mean coordination number of small and large component both increase with the increase of the volume fraction of small component, and the trend is more apparent for large component. However, the overall mean coordination number is essentially a constant and independent of porosity or volume fraction for the binary packing under gravity.