The characteristics of poorly sorted turbidity currents are investigated by numerical simulation. A multiphase approach is utilized to express the mass and momentum conservation equations for the bulk fluid. The Exner equation for multiple size classes of sediment is solved for the evolution of the bottom boundary. The model is applied to simulate experiments on poorly sorted gravity currents and reproduced the vertical structures of velocity, sediment concentration of individual size class and the total deposition depth satisfactorily. The numerical simulation further reveals that the normalized vertical profiles of concentration of all size classes coincide at the position where the maximum longitudinal velocity occurs. Below this position, in the logarithmic velocity region, all concentration profiles are upwardly convex and coarser particle size classes are of larger concentration; above it, in the exponentially decaying velocity region, all concentration curves are upwardly concave and finer particle size classes are of higher concentration. The model also predicts that the position of maximum longitudinal velocity corresponds to a region of low turbulent kinetic energy. The model has also been applied to study three-dimensional poorly sorted depositional turbidity currents debouching from a straight channel into a horizontal unconfined area. Model results reveal the levee and channel building process in which the channel bed slope aggrades at a faster rate than that in the overbank area. The simulation also shows that the contour of mean size of deposited sediment is closely related to the contour of deposit thickness, and elongated somewhat in the flow direction.