A projector Monte Carlo method based on Slater determinants (PMC-SD) is expanded to excited state calculations. Target excited states are calculated state-by-state by eliminating the components of the lower states from the imaginary-time propagator. Test calculations are performed for the singlet excited states of H2O and LiF. As the calculations of H2O show, the accuracy of the PMC-SD method is improved systematically by increasing the number of walkers. The full-CI energies are obtainable as a limit for a given basis set. The avoided crossing of covalent and ionic states in the dissociation of LiF is well reproduced using the PMC-SD method. (C) 2009 Elsevier B.V. All rights reserved.