A hybrid monofilament/braided surgical suture that combines a monofilament with a braided construction. The hybrid surgical suture may be formed by braiding yarns of high tenacity fibers tightly over a core in the form of a monofilament yarn. The monofilament may be any type of material, for example, a nylon, silk, polyester, polyethylene or polypropylene filament, among many others. The stiffness properties of the hybrid surgical suture allow the suture to be pushed through small and very small diameter tubes and cannulations (such as Lasso instruments, for example) yet fix securely with existing fixation devices (such as knotless suture anchors).