Particle packing densification due to vibrations is a common process that occurs in many industrial applications and is beneficial for achieving better mechanical properties in powder metallurgy. However, most of the research up to this point was focused on vibration compaction of uniform-sized or binary particle mixtures, while most actual commercial powders consist of particles of variable sizes. In this work, the packing of multi-sized sphere mixtures under horizontal vibrations is simulated with the help of the discrete element method (DEM). The variations of total and local packing density with vibrations and particle size were investigated. The simulation results suggest that there are optimal values for the two vibration parameters at which the closest packing is obtained. Further increase in the particle size decreases the density and slightly shifts these peaks to the lower values of vibrations. Local density values are quite uniform at the optimal vibration parameters, but the deviations become higher when frequency or amplitude is too low or high. With an increase in particle size, these trends become less profound and more deviated. The investigations of effects of size can help in predicting optimal parameters and density values for experimental studies. These developments are similar to those for uniform and binary particle assemblies and correlate with experimental and numerical studies from the literature. The results can be helpful in carefully choosing the particle mixture properties and vibration conditions for actual manufacturing.