The crystallization (disorder-order transition) of monosized spheres under three-dimensional (3D) mechanical vibrations is studied using discrete element method (DEM). The crystallization dynamics and final structure are analyzed for two selected conditions: i.e. the packing of rough spheres (glass beads) with interval vibration and batch-wise feeding (Case I) and the packing of smooth spheres with continuous vibration and total feeding (Case II). The final packing densities are 0.728 and 0.712 for Cases I and II, respectively, higher than that of random close packings. Partial crystallization characterized by the 111 -oriented face centered cubic (FCC) structure can be observed in both packings, which is further confirmed from the analyses of coordination number, radial and angular distribution functions, and Q6 bond order. Through the tracing of the particles (e.g. the evolutions of velocity and force fields), two crystallization mechanisms are identified: engulfed growth of two adjacent small crystals and epitaxial growth from existing ordered structures (nuclei).