We extend the scalar curvature pinching theorems due to Peng-Terng, Wei-Xu and Suh-Yang. Let M be an n-dimensional compact minimal hypersurface in Sn+l satisfying S f4 -f32 ≤ 1/n S3 , where S is the squared norm of the second fundamental form of M, and fk =∑iλki and λ1(1 ≤ I ≤ n) are the principal curvatures of M. We prove that there exists a positive constant δ(n)(≥ n/2) depending only on n such that if n ≤ S ≤ n +δ(n), then S ≡ n, I.e., M is one of the Clifford torus Sk(√k/n) × Sn-k(√n-k/n) for 1 ≤ k ≤ n - 1. Moreover, we prove that if S is a constant, then there exists a positive constant τ(n)(≥ n - 2/3) depending only on n such that if n ≤ S ＜ n + τ(n), then S ≡ n, I.e., M is a Clifford torus.