We study distribution of particles in Bose-Einstein condensation and ground state energy of condensate by solving a G-P equation with Fourier-Grid-Hamiltonian(F-G-H) method. It is shown that particle density in condensate center increases and radius of condensate decreases as intensity of power-law potential or frequency of harmonic potential is increased or repulsive interaction between particles is decreased. The ground state energy of BEG increases with increasing of total particle number, repulsive interaction between particles, frequency of harmonic potential or intensity of power-law potential. Thomas-Fermi approximation results approximate to numerical results as particle number increases. It is shown that Thomas-Fermi approximation is a good method with large particle numbers. For less particle numbers, numerical method should be used.