In this work we suggest the name “multifractional semimartingale” for a recently proposed stochastic process by proving that this semimartingale has long-range dependence property when the local Holder function bigger than a half.Moreover,we apply the multifractional semimartingale to the stochastic Gilpin-Ayala model driven by the Liouville-type multifractional Brownian motion.Precisely,we prove the existence of the solution of this model in a Sobolev space and present the explicit expression of this solution.