The energy band structure of quantum wires with both Rashba and Dresselhaus spin-orbit couplings in a magnetic field is studied theoretically. We find that the magnetic field strongly affects the subband structure of the wire. With both couplings we obtain a beating pattern in the magnetoresistance. Compared with the quantum wire with only Rashba spin-orbit coupling, the beating pattern can be suppressed even if the coupling strengths are large. This is due to the interplay of the two spin-orbit couplings. The disappearing threshold of the nodes depends on both coupling strengths. When the coupling strengths change, the number of nodes of the beating pattern also varies.