We study the MSW effect when neutrinos are the Majorana particles with a nonvanishing CP-violating phase using the method based on the neutrino energy eigenstates in a medium with varying density. We calculate the transition probability P(nu(e) --> nu(e)) as a function of the ratio of neutrino energy to neutrino mass difference E/Delta(0) in the solar neutrino case for several values of the mixing angle theta and the CP-violating phase sigma. We observe that the overall shape of the transition probability is not affected by the phase sigma.