Based on Bogoliubov’s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U(1) symmetry breaking term √V(λa0 + λ*a0+) to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose-Einstein condensation(BE3 occurs if and only if the U(1) symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schrodinger eigenvalue equation and using the self-consistent condition.