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To improve the shock-capturing capability of the third-order WENO scheme and enhance its computational efficiency, in this paper, we designed a new WENO scheme independent of the local smooth factor, WENO-SIF. The weight functions of the WENO-SIF scheme are segmentation functions of the sub-stencils, which can guarantee it achieves the desired accuracy at the high-order critical points. During the calculation, WENO-SIF need not calculate the smoothing factor, which can effectively reduce the computational consumption. The new WENO-SIF is compared with WENO-JS and other WENO schemes for numerical experiments at one-and two-dimensional benchmark problems with a suitable choice of λ = 0.13. The results show the WENO scheme can further improve the resolution of WENO-JS, achieve the optimal accuracy at high-order critical points, and significantly reduce computational consumption.