An improved Gerchberg-Saxton (GS) algorithm for constructing fully continuous phase plate for beam shaping is proposed. The continuity of the phase plate can be ensured by use of phase unwrapping algorithm and Fourier filter operation,and a better far-field intensity profile can be obtained when the objective amplitude is replaced with a proper modified amplitude function during iteration. The simulation test proves that the method has resolved the conflict between the demand of the phase continuity in the phase plate designing and the optimization of the target beam intensity profile. The demand of the distribution continuity for beam smoothing element,good profile of the target beam and high energy centrality in inertial confinement fusion can be satisfied simultaneously by this algorithm.