A transient 1D model was developed for simulating the dynamics of Liquid encapsulated Czochralski (LEC) growth processes. The model considers a melt-solid flat interface and a uniform temperature within the four phases (i.e., air, melt, solid and encapsulant) and predicts the crystal shape evolution during growth given the time histories of the heater temperature and of the pull rate. The model predictions were satisfactorily compared with experimental InP LEC dynamic growth data. Then, a feedback-feedforward control algorithm effective to achieve a cylindrical growth of single crystals in LEC systems was developed. In particular, the model to be used in the feedforward step was derived linearizing the above dynamic model. The controller keeps the crystal radius constant by acting on the heater, taking as input variables heater and air temperature, crystal weight, seed and crucible position. Controller performances have been tested on a transient model of LEC process as controlled system.