How to detect influential customers to broadcast advertisements to the maximum range is a key issue in effective viral marketing. If multiple companies sell the same product in viral marketing campaigns, there was competition between them. There may exist some unwanted users who hold hostile opinions, and these users may have a negative effect upon receiving promotional information. The company does not want the advertising information to reach such unwanted users over a period of time. In such competitive advertising, how to propagate the positive influence of its product and avoid it reaching the unwanted users of competitors in the limited time is a critical problem for business product promotion. Motivated by the phenomenon, we study the influence maximization problem with limited unwanted users (IML) in the independent cascade (IC) model. To accelerate the process of the influence propagation simulation, we present a path sampling approach based on the random walk to simulate the process of influence propagation. To avoid the unwanted users, only the influences on the paths reaching the wanted users are calculated at each time step, and the influences reaching the unwanted users are ignored.To reduce the computation time, the paths of the random walk will be recorded to avoid repeated random walks in the subsequent seed selection. To find the optimal influential customers, we employ a greedy scheme to select the top-k most influential nodes as seed nodes. Experimental results over the real-world datasets show that the algorithm we presented can get wider effective influence spreading than other algorithms.