The present paper aims to investigate the transport of suspended sediment in an open channel turbulent flow. The method of moments is used to solve the unsteady two-dimensional suspended sediment transport equation where the moment equations are evaluated using a standard finite difference implicit scheme. The distribution of concentration is obtained using the Hermite polynomial representation of central moments. The solution exists for arbitrary form of eddy diffusivity and in contrast to other existing works, the present model considers the most general boundary condition at the channel bed which may be absorbing, reflecting or both. According to such nature of channel bed, the transport process has been distinguished into two phases, viz., suspension phase and deposition phase together with re-entrainment of particles. The model in its present form can be well applicable for sediment transportation in environmental processes. © 2021, The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature.