We theoretically study the effect of the applied magnetic field on the scattering properties of the nanowire surface plasmons coupled to two quantum dots. The dispersion relations of the surface plasmon are found to be upwardly displaced in the presence of an applied magnetic field. The symmetric double peaks in the transmission spectrum resulting from the interference between the localized and delocalized channels of the surface plasmon can combine together and the associated Fano lineshape will be smeared out when increasing the magnitude of the magnetic field.