In this study, the longitudinal wave characteristics of magnetic field sensitive viscoelastic rods under the transverse magnetic field effect is addressed by including lateral inertia effect. The analysis is based on the Love rod theory. The polymeric rod is modeled as standard linear solid viscoelastic material. The obtained explicit solution is illustrated graphically. The comparative results of the analysis show that the transverse magnetic field has a remarkable effect on the wave phase velocity and attenuation coefficient. The transverse magnetic field especially leads to a significant reduction on attenuation coefficient for high frequencies values and large diameters. The analysis results presented here especially for low frequencies ranges can provide a reliable support for the similar experimental studies in related the magnetic field effects.