Given the popularity of the viral marketing campaign in online social networks, finding an effective method to identify a set of most influential nodes so to compete well with other viral marketing competitors is of upmost importance. We propose a "General Competitive Independent Cascade (GCIC)" model to describe the general influence propagation of two competing sources in the same network. We formulate the "Competitive Influence Maximization (CIM)" problem as follows: Under a prespecified influence propagation model and that the competitor's seed set is known, how to find a seed set of $k$ nodes so as to trigger the largest influence cascade? We propose a general algorithmic framework TCIM for the CIM problem under the GCIC model. TCIM returns a $(1-1/e-ε)$-approximate solution with probability at least $1-n^{-\ell}$, and has an efficient time complexity of $O(c(k+\ell)(m+n)\log n/ε^2)$, where $c$ depends on specific propagation model and may also depend on $k$ and underlying network $G$. To the best of our knowledge, this is the first general algorithmic framework that has both $(1-1/e-ε)$ performance guarantee and practical efficiency. We conduct extensive experiments on real-world datasets under three specific influence propagation models, and show the efficiency and accuracy of our framework. In particular, we achieve up to four orders of magnitude speedup as compared to the previous state-of-the-art algorithms with the approximate guarantee.