A boy wants to make friends with a pretty girl. He feels that he may get rejected if he invites her directly. In this situation, what he could do is to influence the girl's friends. Similar situations may occur in social activities. Based on this background, we formulate a new optimization problem, the Target Influence Maximization (TIM) problem and show that this problem can be solved in polynomial-time in networks with no directed cycles. Motivated by this, we study a special strategy to construct solutions for TIM, i.e., The Target Influence Maximization through Sub graph without Directed Cycle (TIMSDC). Two polynomial-time approximation algorithms are designed for TIMSDC. Through extensive experiments on real-world data sets, we demonstrate that our algorithms work efficiently and outperform existing methods.