In this work, MgB2 whiskers were fabricated on a copper substrate by using the hybrid physical-chemical vapor deposition, which was one of the most effective ways to make high quality pure MgB2 films, with the possible growth mechanism discussed. The whiskers are hexagonal and conelike and grow along the [0001] direction with a single-crystal structure. The onset transition temperature is similar to 39 K, which is among the best in the published nanostructure MgB2 papers. Fabrication of nanoscale MgB2 whiskers provides the fundamental understanding of the effect of dimensionality and size on superconductivity.