A novel rheological measuring apparatus was designed by the authors, which introduced an additional sinusoidal vibration in parallel on the extruding direction of polymer melt and was called as Constant Velocity Dynamic Capillary Rheometer in this article. After introducing different melt extrusion speeds and different intensities of vibration, the rheological measuring experiments for a LDPE melt were done respectively by using above-mentioned apparatus, and a mathematical model for the primary normal stress difference of polymer melt under the action of vibration was set up accordingly. Then, the change laws of die swell ratio and those of the primary normal stress difference under different frequencies and amplitudes of vibration were obtained. Compared with the stable state extrusion, after introducing an additional sinusoidal vibration, the die swell ratio and the primary normal stress difference of polymer melt are all decreased obviously.