We propose a high-order conservative method for the nonlinear Schr(o)dinger/Gross-Pitaevskii equation with timevarying coefficients in modeling Bose-Einstein condensation (BEC).This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method,finely describes the condensate wave function and physical characteristics in some small potential wells.Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method.Moreover,it preserves several conservation laws well and even exactly under some specific conditions.