In this paper we present a modified seventh-order weighted essentially nonoscillatory scheme for hyperbolic conservation laws. Local smoothness indicators are constructed based upon Lagrange’s interpolation polynomial. We constructed a new high-order global smoothness indicator to guarantee the scheme achieves optimal order of accuracy at critical points. We investigated this scheme at critical points and verified its order of convergence with the help of linear scalar test cases. We implemented it to various nonlinear scalar equations and system of Euler equations in one- and two-dimensions to demonstrate the discontinuity capturing and high resolution properties of the modified scheme.