The expression of Gaussian envelope solitonin Schrdinger equation is given and proved. According to the Gaussian envelope soliton, Gaussian envelope soliton interaction situation existing in Schrdinger equation is further proposed. The symplectic algorithm for solving Schrdinger equation is proposed. The Schrdinger equation is transformed into the standard Hamiltonian canonical equation by separating the real and imaginary parts of wave function, and the symplectic algorithm is implemented by using Euler center difference separation for the canonical equation. The conserved quantity of symplectic algorithm is given, and its stability is proved. The numerical simulation is carried out on Gaussian envelope soliton motion and multi-soliton interaction in Schrdinger equation. Experimental results prove the correctness of the proposed method and validity of symplectic algorithm.