We investigate theoretically and with three-dimensional particle-in-cell simulations high-quality laser proton acceleration for oblique incidence of the high intensity laser pulse on a double-layer target. The double-layer target is composed of a high-Z ion layer coated by a thin and narrow hydrogen patch. The highest proton energy gain is achieved at a certain incidence angle at which the fast proton maximum energy is much greater than the case of normal incidence. The fast protons form a tilted bunch which propagates at some angle with respect to the normal of the target surface, as determined by the proton energy and the incidence angle.