Based on the nonequilibrium Green's function formalism and density-functional theory, we investigate the onset of electrical rectification in a single C59N molecule in conjunction with gold electrodes. Our calculations reveal that rectification is dependent upon the anchoring of the Au atom on C59N; when the Au electrode is singly bonded to a C atom (labeled here as A), the system does not exhibit rectification, whereas when the electrode is connected to the C-C bridge site between two hexagonal rings (labeled here as B), transmission asymmetry is observed, where the rectification ratio reaches up to 2.62 at ±1 V depending on the N doping site relative to the anchoring site. Our analysis of the transmission mechanism shows that N doping of the B configuration causes rectification because more transmission channels are available for transmission in the B configuration than in the A configuration.