We study the following fractional Choquard equation ε 2 s ( − ∆ ) s u + V ( x ) u = ε − µ ( K µ ∗ F ( u ) ) F ′ ( u ) , x ∈ R N , where ε>0 is a small parameter, s∈(0 ,1), N⩾3, µ∈(0 ,N), F ∈ C 1 ( R , R ) , K µ is the Riesz potential. By applying a new variational approach, under some appropriate conditions on V( x), we obtain there exist at least cupl ( V ) + 1 solutions to the above equation when ϵ→0. In addition, we have demonstrated that the concentration behavior of positive solutions occurs around V as ϵ→0, where V is the set where the potential attains its minimum values.