Optical solitons are concerned for their widely applications in medical image processing, ultrafast optics and optical communications. In this paper, the nonlinear Schrodinger equation (NLSE), which can be used to describe the soliton propagation in those application systems, is investigated. Using symbolic computation, the bilinear forms and analytic soliton solutions are obtained with the bilinear method. Stable propagation of optical solitons is presented, and the influences of related parameters on the optical soliton propagation are discussed. Results have basic theoretical value for the study of optical solitons in fiber lasers.