Influence maximization (IM) is one of the fundamental problems in the area of influence propagation in social networks. Recent studies in influence maximization have primarily focused on the diffusion of single influence. In this thesis, we study the problem under a new diffusion model named Competing General Threshold (CGT) model, which discovers k most influential nodes as early adopters of technology A (e.g., Apple) in a market where a competing technology B (e.g., Blackberry) already exists along with a set of early adopters of technology B. To solve IM under the diffusion of two influences, we first define the CGT diffusion model, then estimate both A and B influence probabilities by using Maximum-Likelihood Estimation from Twitter networks. Next, we propose a new algorithm named cgtMineA to find k influential A-seeds under the CGT model. Experimental results on Twitter networks show that our approach outperforms CELF.