Abstract: The risk of coal and gas outburst is influenced by several factors,and there is a certain correlation among the factors,which lead to a certain extent overlap among the factors in coal and gas outburst risk analysis.Using the principal component analysis,several unrelated comprehensive indexes are combined by each influenced factor,and the mathematical model of coal and gas outburst risk evaluation is established,which simplifies the data analysis of coal and gas outburst risk evaluation,and provides a basis for objective and accurate evaluation of coal and gas outburst risk.