The steady and unsteady laminar mixing processes agitated by a plate impeller in a cylindrical vessel are computed using a Lagrangian particle method based on the Moving Particle Semi-implicit (MPS) technique. By adopting a novel procedure designed previously to compute the mixing rate in the context of the Lagrangian particle method, it is observed that the mixing performance is strongly dependent on the initial configuration of the mixing interface dividing the fluids. For equivolume mixing, steady mixing is found to be more prominent in mixing fluids initially located in a separate semicircle compartment (side-by-side fluid configuration), while unsteady mixing is better in mixing fluids that initially resided in a separate annulus (annular fluid configuration). The fluid particles that initially concentrated near the center region experience a more rapid detachment from the impeller's tip (hence rapid mixing) in the steady mixing case due to the consistent centripetal force originated by the steady rotation. Difficulties in radial mixing, particularly for those fluids residing near the vessel wall, however, are observed for the case of steady mixing, and this issue is circumvented by introducing certain unsteadiness on the rotational velocity of the impeller's tip (unsteady mixing), which may serve as an alternative in replacing baffles in promoting radial flows near the vessel.