In this paper, we introduce an extragradient method to approximate a common solution of variational inequality problem and a fixed point problem for an asymptotically nonexpansive mapping in a real Hilbert space. We prove that the sequence generated by the iterative algorithm converges strongly to a common solution of a variational inequality problem and the fixed point problem for an asymptotically nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in the literature. Some applications of main results are also provided.