In this paper, we investigate the bright solitons on a cnoidal wave background train of the inhomogeneous nonlinear Schrödinger equation, which may be applicable to many physically realizable systems such as Bose-Einstein condensation media and plasma, etc. We use well-known methods to reduce the inhomogeneous nonlinear Schrödinger equation to a standard nonlinear Schrödinger equation by using the combination of Husimi's and Lens-type transformations. We study the superposed configuration of soliton with a cnoidal wave solution of the underlying equation. Finally, we discuss the dynamics of soliton on a cnoidal wave background in Bose-Einstein condensation trapped in linear density and harmonic density profiles separately. © 2008 IOP Publishing Ltd.