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• An imputation model imputes specific missing values in multivariate time series. • Our method outperforms the comparison method when specific values are missing. • Our experiments provide selection principles of hyperparameters. • Our experiment determines the best training method with introduction of noise. Data missing is a ubiquitous phenomenon in multivariate time series analysis because of failure measurements, improper installation or other unfavorable factors. Most imputation methods, such as statistical methods and machine learning methods, are mainly for dealing with random or continuous missing, but do not take into consideration the non-random specific missing situation. This paper proposes an imputation model based on the variational auto-encoders (VAE) and shift correction for specific missing values, which is also extended to the β -VAE model. The shift correction is used to correct the original probability distribution deviation caused by specific values concentrated missing. Then taking the meteorological and air quality data sets in Beijing as the example, this paper mainly explores two common specific missing situations, including large values missing and small values missing. The experimental results show that the proposed model can effectively impute specific missing values, which has high imputation accuracy and robustness. [ABSTRACT FROM AUTHOR]