An anchor system for securing a lead to a patient's skull is disclosed. The lead is of the type that passes through a burr hole created in the patient's skull and includes a distal end which is implanted within the patient's brain at a target site. The anchor, according to a first embodiment of the invention includes a stem, an integrally formed rim plate, and a peripheral clamping structure. The clamping structure is adapted to receive and snugly hold a portion of the lead. The stem is sized and shaped to fit within the burr hole, leaving the rim plate positioned flush with the patient's skull. A flared passage is provided within the stem and rim plate so that the lead may pass through the stem and into the rim plate, at which point the lead follows the contours of the flared passage and communicates with the peripheral clamping structural. The clamping structure holds a portion of the lead so that any tension of the lead will not be transmitted past the anchor and the distal end of the lead will not become displaced from the target site. According to a second embodiment, the peripheral clamping structure includes several flexible loops that are sized and spaced from each other to allow a lead to be laced through the loops as the lead extends about the periphery of the rim plate.