Closed-loop operation of superconducting magnets can significantly reduce cryogenic heat load and enhance magnetic field stability, which has been widely applied in systems such as magnetic resonance imaging (MRI) and electro-dynamic suspension (EDS). Quench detection for close-loop superconducting magnets, especially high-Tc superconducting (HTS) magnets, has long been a challenging issue. In this paper, we derived quench-induced currents redistribution characteristics in parallel co-wound closed-loop superconducting magnets, and proposed a current-redistribution based quench detection method for such magnets. Artificial quench tests on a small scale co-wound closed-loop HTS coil were staged, with AC background magnetic field applied to simulate tough working conditions such as in HTS maglevs and HTS machines. Results show that the method can sensitively and reliably detect a quench even at its inception, long before the coil field change becoming identifiable, and the method is robust against background AC magnetic fields. This work may potentially be useful for reducing the quench damage risk in closed-loop superconducting magnet for various applications.