Influence maximization has attracted a considerable amount of research work due to the explosive growth in online social networks. Existing studies of influence maximization on social networks aim at deriving a set of users (referred to as seed users) in a social network to maximize the expected number of users influenced by those seed users. However, in some scenarios, such as election campaigns and target audience marketing, the requirement of the influence maximization is to influence a set of specific users. This set of users is defined as the target set of users. In this paper, given a target set of users, we study the Target Influence Maximization (TIM) problem with the purpose of maximizing the number of users within the target set. We particularly focus on two important issues: (1) how to capture the social influence among users, and (2) how to develop an efficient scheme that offers wide influence spread on specified subsets. Experiment results on real-world datasets validate the performance of the solution for TIM using our proposed approaches.