We report a new kind of experimental realization of a molecular rectifier, which is based on a single azafullerene C59N molecule in a double-barrier tunnel junction via the single electron tunneling effect. An obvious rectifying effect is observed. The positive onset voltage is about 0.5-0.7 V, while the negative onset voltage is about 1.6-1.8 V. Theoretical analyses show that the half-occupied molecular orbital of the C59N molecule and the asymmetric shift of the molecular Fermi level when the molecule is charged are responsible for the molecular rectification.