Nowadays, social networks are considered as the very important medium for the spreading of information, innovations, ideas and influences among individuals. Viral marketing is a most prominent marketing strategy using word‐of‐mouth advertising in social networks. The key problem with the viral marketing is to find the set of influential users or seeds, who, when convinced to adopt an innovation or idea, shall influence other users in the network, leading to a large number of adoptions. In this study, we study the competitive viral marketing problem from host perspective, where the host of the social network (such as Facebook, Twitter, etc.) sells the viral marketing campaigns to its customers and keeps control of the allocation of seeds. Seeds are allocated by creating ‘bang for the buck’ for each company. In this paper, we first propose a new influence diffusion model considering both negative and positive influences. Subsequently, we propose a novel optimization problem, named Blocking Negative Influential Node Set (BNINS) selection problem, to identify the positive node set (seeds) such that the number of negatively activated nodes is minimised for all competitors. Finally, we proposed a greedy algorithm called BNINS‐GREEDY to solve BNINS and conducted comprehensive experiments and simulations to validate the proposed method. The results show that, for random graphs, on average, BNINS‐GREEDY blocks the negative influence 17.22 per cent more than the most related work called Competitive Linear Directed Acyclic Graph. Moreover, on the real Epinions dataset, BNINS‐GREEDY achieves 7.6 per cent more positive influence propagation than Competitive Linear Directed Acyclic Graph. Copyright © 2015 John Wiley & Sons, Ltd.