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Microarray experiments on gene expression inevitably generate missing values, which impedes further downstream biological analysis. Therefore, it is key to estimate the missing values accurately. Most of the existing imputation methods tend to suffer from the over-fitting problem. In this study, we propose two regularized local learning methods for microarray missing value imputation. Motivated by the grouping effect of L2 regularization, after selecting the target gene, we train an L2 Regularized Local Least Squares imputation model (RLLSimpute_L2) on the target gene and its neighbors to estimate the missing values of the target gene. Furthermore, RLLSimpute_L2 imputes the missing values in an ascending order based on the associated missing rate with each target gene. This contributes to fully utilizing the previously estimated values. Besides L2, we further explore L1 regularization and propose an L1 Regularized Local Least Squares imputation model (RLLSimpute_L1). To evaluate their effectiveness, we conducted extensive experimental studies on six benchmark datasets covering both time series and non-time series cases. Nine state-of-the-art imputation methods are compared with RLLSimpute_L2 and RLLSimpute_L1 in terms of three performance metrics. The comparative experimental results indicate that RLLSimpute_L2 outperforms its competitors by achieving smaller imputation errors and better structure preservation of differentially expressed genes.