In this work, we use Lewenstein’s theory to calculate the high order harmonic spectra of CO molecule in a linearly polarized laser field combined with an external electrostatic field. The results show that the characteristics of the high order harmonic spectra of CO molecule depend strongly on the direction of the external static electric field relative to the orientation of CO. Especially, when the direction of the external static electric field points from O to C, the plateau of the harmonic spectrum becomes wider and the cutoff frequency reaches a larger value than the scenario without external static electric field. When the direction of the external static electric field points from C to O, the harmonic spectrum shows a double-plateau structure. Using Lewenstein theory, these phenomena can be understood from the viewpoint that the harmonic generation comes from a coherent superposition of the contributions of two kinds of channels characterized by C-end ionization and O-end ionization. The C(O)-end ionization channel means that the electron is ionized from C(O) end, then accelerated by the driving electric field, finally recombines with its parent molecular ion at either C or O end, emitting the harmonics. For the same harmonic order, the contribution of the C-end ionization channel is greater than that of the the O-end ionization channel. The two kinds of channels emit harmonics in adjacent half period of laser, where the external static electric field causes the cutoff frequency of the harmonic spectrum to increase and decrease in the adjacent half period of the laser field. Especially, when the direction of external static electric field is from the C to O, the cutoff frequency of the harmonic spectrum of the C-end ionization channel decreases, resulting in a higher first plateau in the spectrum. While, the increase of cut-off frequency of the O-end ionization channel will result in a lower second plateau. When the direction of external static electric field is reversed, the cutoff frequency of the harmonics of the C-end channel increases, leading the plateau of CO harmonic spectrum to become wider than that without the external static electric field. The cut-off frequency of the O-end ionization channel decreases. Because the contribution of the O-end ionization channel can be ignored compared with that of C-end ionization channel, the C-end channel dominates the contribution to harmonic generation and hence there is only one plateau in the harmonic spectrum. This work provides a clear physical picture for the formation of a double-plateau structure of CO harmonic spectra under the action of an external static electric field.