Since blur kernel estimation is an ill-posed problem, it is essential that it be constrained by parametric image priors. However, the previous normalized sparsity measure alters the kernel structure during estimation. To address the problem of single-image blur kernel estimation, a local smoothness prior is introduced to the normalized sparsity model to constrain the blurred image gradient to be similar to the unblurred one. Moreover, based on the inequality constraints, a kernel optimization algorithm is proposed to weaken the noise. Experimental results show that the proposed method is robust against noise and is able to estimate a stable blur kernel. It outperforms other state-of-the-art methods on both synthetic and real data.