Recently, in the literature, we can see quite a few papers about general coefficient bounds for subclasses of bi-univalent functions. However, we can find just a few papers about general coefficient estimates for subclasses of bi-close-to-convex functions. In the present study, we give and look into a new subclass of analytic and bi-close-to-convex functions in the open unit disk. Making use of the Faber series, we have an upper bound for the general coefficient of functions in this class. We also demonstrate the invisible behavior of the beginning coefficients of a special subclass of bi-close-to-convex functions.