An endovascular implantable shunt device for draining cerebrospinal fluid from a patient's subarachnoid space includes a shunt having opposed first and second ends, a one-way valve located at the first end of the shunt, a tip disposed at the second end, and a hollow passageway extending between the tip and one-way valve. The tip is constructed to penetrate a patient's sinus wall. Cerebrospinal fluid drains through the tip and out through the valve.