In the paper, we consider the following hemivariational inequality problem involving the fractional Laplacian:{(−Δ)su+λu∈α(x)∂F(x,u)x∈Ω,u=0x∈RN∖Ω,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\textstyle\\begin{cases} (-\\Delta )^{s}u+\\lambda u\\in \\alpha (x) \\partial F(x,u) & x \\in \\varOmega , \\\\ u=0 & x\\in \\mathbb{R} ^{N} \\backslash \\varOmega , \\end{cases} $$\\end{document} where Ω is a bounded smooth domain in mathbb{R} ^{N} with Ngeq 3, (-Delta )^{s} is the fractional Laplacian with sin (0,1), lambda >0 is a parameter, alpha (x): varOmega rightarrow mathbb{R} is a measurable function, F(x, u):varOmega times mathbb{R} rightarrow mathbb{R} is a nonsmooth potential, and partial F(x,u) is the generalized gradient of F(x, cdot ) at uin mathbb{R} . Under some appropriate assumptions, we obtain the existence of a nontrivial solution of this hemivariational inequality problem. Moreover, when F is autonomous, we obtain the existence of infinitely many solutions of this problem when the nonsmooth potentials F have suitable oscillating behavior in any neighborhood of the origin (respectively the infinity) and discuss the properties of the solutions.