The Asian pricing was considered when underlying stock price obeys jump-diffusion process.An arithmetic mean Asian options pricing model and a partial differential equation of the pricing model were established by using the generalized Itô formula and the no-arbitrage principle,based on the method of approximating hedge jump risk.Then,the ultra parabolic partial differential equation was transformed into a generalized parabolic equation by using variable substitution method.The semidiscretization numerical arithmetic scheme of the partial differential equation derived by means of semidiscretization,and the stability and error analysis of the difference scheme were also discussed.Finally,the empirical analysis of Asian option pricing was carried out,taking the Asian-style electricity options,as an example which have been traded in the Nord Pool.