This paper is devoted to investigating particle transport in nonhomogeneous bounded media with [0,vM] energy and anisotropic scattering-fission kernel. The time-dependent equation and the corresponding transport operatorAare discussed in the space of continuous functions. Some aspects of the spectral properties ofA(e.g., the properties of Pas(A) and the dominant eigenvalue ofA, etc.) are considered and the existence-uniqueness of the classical time-dependent solution is obtained. Furthermore, an asymptotic expansion (under the maximum norm) of the time-dependent solution is given and the asymptotic behavior is studied.