The mixed fractional Brownian motion ( mf Bm ) has become quite popular in finance, since it allows one to model long-range dependence and selfsimilarity while remaining, for certain values of the Hurst parameter, arbitragefree. In the present paper, we propose approximate closed-form solutions for pricing arithmetic Asian options on an underlying described by the mf Bm . Specifically, we consider both arithmetic Asian options and arithmetic Asian power options, and we obtain analytical formulas for pricing them based on a convenient approximation of the strike price. Both the standard mf Bm and the mf Bm with Poisson log-normally distributed jumps are taken into account.