Motivation: Cross-species analysis of large-scale protein-protein interaction (PPI) networks has played a significant role in understanding the principles deriving evolution of cellular organizations and functions. Recently, network alignment algorithms have been proposed to predict conserved interactions and functions of proteins. These approaches are based on the notion that orthologous proteins across species are sequentially similar and that topology of PPIs between orthologs is often conserved. However, high accuracy and scalability of network alignment are still a challenge. Results: We propose a novel pairwise global network alignment algorithm, called PrimAlign, which is modeled as a Markov chain and iteratively transited until convergence. The proposed algorithm also incorporates the principles of PageRank. This approach is evaluated on tasks with human, yeast and fruit fly PPI networks. The experimental results demonstrate that PrimAlign outperforms several prevalent methods with statistically significant differences in multiple evaluation measures. PrimAlign, which is multi-platform, achieves superior performance in runtime with its linear asymptotic time complexity. Further evaluation is done with synthetic networks and results suggest that popular topological measures do not reflect real precision of alignments. Availability and implementation: The source code is available at http://web.ecs.baylor.edu/faculty/cho/PrimAlign. Supplementary information: Supplementary data are available at Bioinformatics online.