A compact cold atom beam source based on a multistage two-dimensional magneto-optical trap (MOT) has been demonstrated and characterized. The multiple-stage design greatly reduces the overall size of the source apparatus while providing a high flux of atoms. The cold atom beam was used to load a separate MOT in ultrahigh vacuum, and we obtained an actual trap loading rate of $1.5\times {10}^9\text{\hspace{0.17em} atoms}∕\mathrm{s}$ while using only $20\mathrm{mW}$ of total laser power for the source. The entire source apparatus, including optics, can fit into a $4\mathrm{cm}\times 4\mathrm{cm}\times 13\mathrm{cm}$ volume.