We consider strings moving in the R-t x S-eta(3) subspace of the eta-deformed AdS(5) x S(5)and obtain a class of solutions depending on several parameters. They are characterized by the string energy and two angular momenta. Finite-size dyonic giant magnon belongs to this class of solutions. Further on, we restrict ourselves to the case of giant magnon with one nonzero angular momentum, and obtain the leading finite-size correction to the dispersion relation. (C) 2014 The Authors. Published by Elsevier B.V.