This paper deals with the double power nonlinear Schrodinger equation in one dimension, which is proposed as a model to describe the Bose-Einstein condensate with mixed state interactions. The equation admits unstable solitons in the L ² supercritical case. In terms of Cote , Martel and Merle’s argument, multi solitons of the equation are constructed by using unstable solitons in the L ² supercritical case, which extend Cote , Martel and Merle’s results from the pure power case to the double power nonlinear cases.