Microarray data often contain missing values which significantly affect subsequent analysis. Existing LLSimpute-based imputation methods for dealing with missing data have been shown to be generally efficient. However, all of the LLSimpute-based methods do not consider the different importance of different neighbors of the target gene in the missing value estimation process and treat all the neighbors equally. In this paper, a locally auto-weighted least squares imputation (LAW-LSimpute) method is proposed for missing value estimation, which can automatically weight the neighboring genes based on the importance of the genes. Then, an accelerating strategy is added to the LAW-LSimpute method in order to improve the convergence. Furthermore, an iterative missing value estimation framework of LAW-LSimpute (ILAW-LSimpute) is designed. Experimental results show that the ILAW-LSimpute method is able to reduce the estimation error.