An analytic model has been developed to analyze the residence time distribution of melt in the screw channel of the melt conveying section in a novel extruder of which the screw can vibrate axially. A comparison of the residence time distribution of melt in screw channel with and without vibration shows that the residence time of melt increases with the apply of vibration and the larger the vibration frequency and amplitude are, the longer time it will take the melt to travel through the melt conveying section, which is in favor of the improvement of the effect of melt mixing.