The interference effect in the photdetachment of a diatomic molecular anion is investigated theoretically for different molecular orientation by using the two-center model. An analytic formula is presented for the photodetached electron flux distribution at a given observation plane. Taking $H^-_2$ as an example, we calculate the electron flux distribution and photodetachment cross section for arbitrary molecular orientation. The results show that the molecular orientation has great influence on the photodetachment of the diatomic molecular anion. At certain molecular orientation, the interference in the electron flux distribution is totally constructive; while at some other orientations, the interference is destructive. For molecular orientation along the laser light polarization, the oscillation amplitude in the photodetachment cross section is the largest; however, for the molecular orientation perpendicular to the laser light polarization, no oscillation appears in the cross section. Our studies suggest that we can control the photodetachment process of the molecular negative ion by changing the molecular orientation. Our researches will be helpful for the theoretical and experimental study of the photodetachment of molecular anion.