The implementation of a state-specific configuration-selective vibrational configuration interaction (cs-VCI) approach based on a polynomial representation of the potential energy surface is presented. Advantages over grid-based algorithms are discussed. A combination of a configuration selection criterion, the simultaneous exclusion of irrelevant configurations, and an internal contraction scheme allow to handle large variational spaces. A modified version of the iterative Jacobi-Davidson diagonalization has been used to determine relevant internal eigenpairs of the cs-VCI matrices in the selected space. Benchmark calculations are provided for systems with up to 2 x 10(7) configurations and three-mode couplings in the expansion of the potential. (C) 2009 American Institute of Physics. [doi:10.1063/1.3243862]