Based on the fourth- and sixth-order central compact schemes with tridiagonal coefficient matrix, the fourth- and fifth-order weighted compact nonlinear difference schemes are obtained for solving hyperbolic conservation law equations, the function values of half-node are interpolated with the nonlinear combination of the fifth-order WENO difference scheme of large template and two small symmetrical templates. The computational accuracy and efficiency of the new scheme are verified by the results of linear convection equation. The resolution of the new scheme is verified by the results of one-dimensional inviscid Burgers equation. The ability of the new scheme to capture the shock discontinuity in nonlinear problems is verified by one - and two-dimensional Euler equations. The numerical experiments show that the proposed scheme is an efficient, high-order and high-resolution shock capturing scheme.