The interactions of two-frequency laser with Langmuir wave in a plasma beat-wave acce-lerator are calculated. We show that the development of the Langmuir wave from initial stage to saturation is closely correlated to the evolution of the three waves involved from phase locking to phase mismatching. The phase difference, describing the extent of three-wave coup-ling, is therefore of great importance in Langmuir-wave excitation by beating two-frequency la-ser.