Additive manufacturing (AM) has attracted much attention worldwide in various applications due to its convenience and flexibility to rapidly fabricate products, which is a key advantage compared to the traditional subtractive manufacturing. This discrete element method (DEM) study focusses on the impact of particle polydispersity during the particle spreading process on parameters that affect the quality of the final product, like packing and bed surface roughness. The particle systems include four lognormal particle size distribution (PSD) widths, which are benchmarked against the monodisperse system with the same mean particle diameter. The results reveal that: (i) the solid volume fraction of the initial packed particle bed in the delivery chamber increases then plateaus as the PSD width increases; (ii) regardless of PSD width, the solid volume fraction of the particle bed increases with spreading layer height before compression, but decreases with layer height after compression; (iii) the bed surface roughness increases with PSD width or layer height both before and after the compression of the spreading layer; (iv) the extent of increase in solid volume fraction during compression is correlated with the extent of decrease in bed surface roughness; and (v) the broader PSDs exhibit larger fluctuations of solid volume fraction of the particle bed and bed surface roughness due to greater variability in the arrangement of particles of different sizes. The results here have important implications on the design and operation of particle-based AM systems.