Growth and breakup of pendant drops from the tip of a capillary is of great importance due to its wide applications and the richness of the underlying physics. During the growth and breakup of a pendant drop, the size variation will produce pressure fluctuation in the upstream, which is studied numerically with the level set method to predict the interface. The numerical results are validated against experimental images showing the growth and breakup of pendant drops obtained from a high speed camera. The effects of the surface tension and the outer diameter of the capillary on the amplitude and the period of the pressure fluctuation are examined. Compared to other methods of surface tension measurement, this method shows potential advantages of its good accuracy, simplicity, and low cost.