Genome-wide analysis of transcriptome responses of human cell lines to drug treatments is an important issue in drug discovery. However, drug-induced gene expression profiles are largely unknown for all human cell lines, which is a serious obstacle in practical applications. In this study, we developed a novel computational method to predict unknown parts of drug-induced gene expression profiles on various human cell lines and to predict new drug therapeutic indications for a wide range of diseases. We proposed a tensor-train weighted optimization algorithm to predict the potential values for unknown parts in tensor-structured gene expression data. It was shown that the proposed algorithm can accurately reconstruct drug-induced gene expression data for a range of human cell lines. It was also shown that in comparison with the use of original gene expression profiles, the use of imputed gene expression profiles improved the accuracy of drug repositioning in the framework of multitask learning.