This paper presents a basic study on the characteristics of capillary wave propagation on a water ligament surface. The capillary wave plays an important role in de-stabilizing ligaments created by the turbulent motion of liquid jet. The ligament end contracts due to capillary force and emanates surface waves. The analysis is based on 2D numerical simulation and linear wave analysis, and reveals the basic characteristics such as contraction speed, wave speed and the associated flow field structures. The phenomenon can be parameterized by the Ohnesorge number, and the numerical results are in good agreement with the linear analysis. The higher pressure cases, where the Ohnesorge number is high, will be investigated in the next step.