Aiming at a new incremental stochastic process in double-fractional Brownian motion with Markovian switching，based on the idea of reliability mathematics，the real probability measure is transformed into the equivalent martingale measure by using the measure transformation technique，and the pricing problem of fixed-price Asian option with continuous time under this model is studied. By using the probability density transfer function satisfied by Asian options，the classical measure transformation method is combined with quasi-martingale method，which is extended to the B-S market driven by double-fractional Brownian motion. The pricing formulas of geometrically average Asian call and put options with fixed execution price are obtained by using risk-neutral pricing method. The double fractional Brown motion is independent and stable incrementally，which is more consistent with the display situation. Compared with the option pricing formula based on fractional Brownian motion，fractional Brownian motion is only a special case of double-fractional Brownian motion，which can be extended to Asian option pricing model based on double-fractional Brownian motion.