In this paper, we study the following nonlinear fractional Schr\documentclass[12pt]{minimal}\begin{document}$\ddot{\mbox{o}}$\end{document}ödinger equation with critical exponent \documentclass[12pt]{minimal}\begin{document}$h^{2\alpha }(-\Delta )^{\alpha }u + V(x)u= |u|^{2_{\alpha }^{*}-2}u + \lambda |u|^{q-2}u, x\in \mathbb {R}^{N}$\end{document}h2α(−Δ)αu+V(x)u=|u|2α*−2u+λ|u|q−2u,x∈RN, where h is a small positive parameter, 0 < α < 1, \documentclass[12pt]{minimal}\begin{document}$2< q < 2_{\alpha }^{*}$\end{document}2<q<2α*, \documentclass[12pt]{minimal}\begin{document}$2_{\alpha }^{*} = \frac{2N}{N- 2\alpha }$\end{document}2α*=2NN−2α is the critical Sobolev exponent, and N > 2α, λ > 0 is a parameter. The potential \documentclass[12pt]{minimal}\begin{document}$V: \mathbb {R}^{N} \rightarrow \mathbb {R}$\end{document}V:RN→R is a positive continuous function satisfying some natural assumptions. By using variational methods, we obtain the existence of solutions in the following case: if \documentclass[12pt]{minimal}\begin{document}$2< q< 2_{\alpha }^{*}$\end{document}2<q<2α*, there exists λ0 > 0 such that for all λ ⩾ λ0, we show that it has one nontrivial solution and there exist at least \documentclass[12pt]{minimal}\begin{document}$cat_{\Lambda _{\delta }}(\Lambda )$\end{document}catΛδ(Λ) nontrivial solutions; if \documentclass[12pt]{minimal}\begin{document}$\max \lbrace 2, \frac{4\alpha }{N-2\alpha }\rbrace < q < 2_{\alpha }^{*}$\end{document}max{2,4αN−2α}<q<2α*, then there is one nontrivial solution and there exist at least \documentclass[12pt]{minimal}\begin{document}$cat_{\Lambda _{\delta }}(\Lambda )$\end{document}catΛδ(Λ) nontrivial solutions for all λ > 0.