In this paper, we obtained best proximity coincidence point theorems for α-Geraghty contractions in the setting of complete metric spaces by using weak P-property. Also we presented some examples to prove the validity of our results. Our results extended and unify many existing results in the literature. Moreover, in the last section as applications of our main results, we can apply some coincidence best proximity point and coupled coincidence proximity point on metric spaces endowed with an arbitrary binary relation.