Based on the research on transport phenomenon of fractional Brownian motor, a systematic parameter (i.e. symmetry parameter) which describes the asymmetry of the periodic potential field is introduced, and the influences of the symmetry parameter and the memory parameter (i.e. the fractional order) on the transport behavior are also investigated. The numerical results show that the combined effect of fractional order and symmetry parameter can result in the reverse flow of Brownian particle's transport, and the fractional order corresponding to the maximal averaged velocity is irrelevant to the frequency of the external periodic force, but it will still increase monotonically as the symmetry parameter increases.