We investigate the effects of Rashba spin-orbit interaction on the electronic energy dispersion and zero-temperature ballistic conductance of double quantum wire under the influence,of perpendicular magnetic field. The wire system is represented by a symmetric, double quartic-well confinement potential. Numerical results reveal that competing effects between spin-orbit interaction and magnetic field modify strongly the energy subband structure and introduce anticrossings between subbands. Moreover, it is found that the conductance character of a quasi-one-dimensional ballistic conductor, which is closely related to the energy-dispersion spectrum, is very sensitive to the shape of potential profile, magnetic field and Rashba spin-orbit coupling. (C) 2015 Elsevier Ltd. All rights reserved.