Granular packing structures of cohesive microsized particles with different sizes and size distributions, including monosized, uniform, and Gaussian distribution, are investigated by using two different history dependent contact models with discrete element method (DEM). The simulation is carried out in the framework of liggghts, which is a DEM simulation package extended based on branch of granular package of widely used open-source code LAMMPS. Contact force caused by translation and rotation, frictional and damping forces due to collision with other particles or container boundaries, cohesive force, van der Waals force, and gravity is considered. The radial distribution functions (RDFs), force distributions, porosities, and coordination numbers under cohesive and noncohesive conditions are reported. The results indicate that particle size and size distributions have great influences on the packing density for particle packing under cohesive effect: particles with Gaussian distribution have the lowest packing density, followed by the particles with uniform distribution; the particles with monosized distribution have the highest packing density. It is also found that cohesive effect to the system does not significantly affect the coordination number that mainly depends on the particle size and size distribution. Although the magnitude of net force distribution is different, the results for porosity, coordination number, and mean value of magnitude of net force do not vary significantly between the two contact models.