The drilling cutting gas desorption index △h2 is one of the most important indexes for the prediction of coal and gas outburst. Based on the mathematical and physical model of the gas diffusion of coal particles, the analytical solution of △h2 was deduced. The relationship between the drilling cutting gas desorption index △h2 and parameters of gas occurrence such as the gas diffusion coefficient, adsorption constants (a and b), gas pressure, and gaSubscript textSubscript texts content were studied. The results show that △h2 increases and gas diffusion resistance decreases with the gas diffusion coefficient. The drilling cutting gas desorption index △h2 increases with the adsorption constant a, and the two meet the linear relationship. △h2 increases with the adsorption constant b and the raising rate gets lower gradually. And, △h2 increases with the gas pressure, and the two meet the power relationship with very high correlation coefficient.△h2 and gas content are in linear relationship.