The measurement error of Coriolis mass-flow meter is based on the vibration characteristics of the elastic tube of flow meter. In this paper, the influence of pulsating flow on performance of Coriolis mass-flow meter is analyzed, with the straight tube Coriolis mass-flow meter as the investigated object. The mathematical model of vibration of straight tube Coriolis mass-flow meter under pulsating flow is established. By making use of Galerkin method, the model is converted into a coupled multi-degree system under combined parametric and forcing excitation. Multiscale method is used to analyze qualitatively the discrete multi-degree system, the main vibrational components of the tube under pulsating flow are given, and thus the mechanism of action of pulsating flow to Coriolis mass-flow meter is shown clearly. Most of conclusions obtained here have been testified by experiments that were reported in the published papers. The conclusions are helpful to further investigation and application of Coriolis mass-flow meter.