Under investigation in this paper is an inhomogeneous nonlinear Schrodinger equation, which describes the propagation of a large-wavelength small-amplitude electron plasma wave in a parabolic-distributed and constant-interactional-damping inhomogeneous plasma. Via the Hirota method, Bell-polynomial approach and symbolic computation, bilinear form, Backlund transformation and N-soliton solutions are obtained. Influence of the linear density coefficient a and damping coefficient beta on the soliton envelopes is also discussed, i.e. a can affect the soliton position, while beta is related to the soliton intensity, velocity and phase shift. Periodically attractive and repulsive interactions are shown. Asymptotic analysis shows that the interactions between/among the solitons are elastic.