In this talk, we consider center stable manifolds of unstable line solitary waves for the Zakharov--Kuznetsov equation on a cylindrical space and show the stability of the unstable line solitary waves for initial datum on the center stable manifolds, which yields the asymptotic stability of unstable solitary waves on the center stable manifolds near by stable line solitary waves. To construct the center stable manifolds, we apply Hadamard's graph transform approach by Nakanishi--Schlag'12. To treat the nonlinear term of the Zakharov--Kuznetsov equation, we use the bilinear estimate on Fourier restriction spaces by Molinet--Pilod'15. Since generalized eigenfunctions of the dual operator of the linearized operator of the Zakharov--Kuznetsov equation around line solitary waves with respect to the 0 eigenvalue is not $L^2$ function, we can not show directly the estimate to get a contraction map on a set of graphs by using the mobile distance which was introduced by Nakanishi--Schlag'12. Modifying the mobile distance by Nakanishi--Schlag'12, we construct a contraction map on the graph space.