A three-dimensional Lattice Boltzmann flow and scour model is developed to simulate time-dependent scour below a submarine pipeline. The proposed model presented in this paper is able to predict streamwise and spanwise propagations of scour with respect to lattice unit of time. It is evident from this study that the existence of a spiral vortex in the proximity of the span shoulder is quite noteworthy. It is revealed that the critical regime of the 2-D scour process is found to be up to one pipe diameter away in both directions from the middle of the unsupported length of pipelines. The equilibrium maximum scour depth and the shape of streamwise equilibrium scour hole compare well with the available experimental data. The speed of propagation of scour along the pipeline length maintains an almost constant rate, which is consistent with the experimental observations found in literature. In addition, it is seen that the scour slope at the shoulder region remains fairly constant throughout the whole scour process.