To determine the Turán numbers of even cycles is a central problem of extremal graph theory. Even for C 6, the Turán number is still open. Till now, the best known upper bound is given by Füredi, Naor and Verstraëte [On the Turán number for the hexagon, Advances in Math.]. In 2010, Nikiforov posed a spectral version of extremal graph theory problem: what is the maximum spectral radius ρ of an H-free graph of order n? Let e x s p (n, H)= max {ρ (G)|| V (G)|= n, H⊈ G}. In contrast to the unsolved problem of Turán number of C 6, we obtain the exact value of e x s p (n, C 6) and characterize the unique extremal graph. The result also confirms Nikiforov’s conjecture [The spectral radius of graphs without paths and cycles of specified length, Linear Algebra Appl.] for k= 2.