Powder-based additive manufacturing is an efficient and rapid manufacturing technique because it allows fabrication of complex parts that are often unobtainable by traditional manufacturing processes. A better understanding of the packing structure of the powder is urgently needed for the powder-based additive manufacturing. In this study, the sequential addition packing algorithm is employed to investigate the random packing of spherical particles with and without shaking effect. The 3D random packing structures are demonstrated by illustrative pictures and quantified in terms of pair distribution function, coordination number, and packing density. The results are presented and discussed aiming to produce the desirable packing structures for powder-based additive manufacturing.