It is common that time-series data with missing values are encountered in many fields such as in finance, meteorology, and robotics. Imputation is an intrinsic method to handle such missing values. In the previous research, most of imputation networks were trained implicitly for the incomplete time series data because missing values have no ground truth. This paper proposes Random Drop Imputation with Self-training (RDIS), a novel training method for imputation networks for the incomplete time-series data. In RDIS, there are extra missing values by applying a random drop on the given incomplete data such that the imputation network can explicitly learn by imputing the random drop values. Also, self-training is introduced to exploit the original missing values without ground truth. To verify the effectiveness of our RDIS on imputation tasks, we graft RDIS to a bidirectional GRU and achieve state-of-the-art results on two real-world datasets, an air quality dataset and a gas sensor dataset with 7.9% and 5.8% margin, respectively.