JLQCD collaboration recently started the Nf = 3 QCD simulations with the O(a)-improved Wilson fermion action employing an exact fermion algorithm developed for odd number of quark flavors. It is found that this theory has an unexpected non-trivial phase structure in the (β, κ) plane even at zero temperature. A detailed study is made to understand the nature of the observed phase transitions and to find the way of avoiding untolerably large lattice artifacts associated with the phase transition.