In this paper, we consider the following nonlinear elliptic equation involving the fractional Laplacian with critical exponent:(−Δ)su=K(x)uN+2sN−2s,u>0inRN, where s∈(0,1) and N>2+2s, K>0 is periodic in (x1,…,xk) with 1≤k<N−2s2. Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in Rk, including infinite lattices. On the other hand, to obtain positive solution with infinite bumps such that the bumps locate in lattices in Rk, the restriction on 1≤k<N−2s2 is in some sense optimal, since we can show that for k≥N−2s2, no such solutions exist.