The dynamics of a single Bose-Einstein condensate soliton in three different kinds of double potentials, namely symmetry double-barrier structure, symmetry double-well structure and mixed structure, with different parameters, are investigated by numerical method. A method for manipulating the position of Bose-Einstein condensate soliton is proposed, and the evolution of two solitons in double-well and double-barrier is studied. The results reveal thata single soliton will exhibit different evolutional behaviors such as oscillation, tunneling and being trapped by potential wells under the double potentials with different parameters, and two solitons will be attracted by the potential well or repelled by the potential barrier when the parameters of the double potential are controlled to appropriate values.