This paper proposes a cost-effective Minimum Cycle Cover (MCC) algorithm derived from Double Cycle Cover (DCC) algorithm for performing Automatic Protection Switching (APS) in optical networks. The architecture in the proposed MCC is each link between two APSs has only a pair of fibers, instead of two pairs of fibers in the DCC. The MCC is used to find the minimum number of recovery cycles (or termed Minimum recovery cycle) based on cycle architecture of the DCC to cover all the links in the planar networks. The MCC algorithm inherits many advantages of the DCC, for example fast, distributed and autonomous, and tolerates multiple failures, but with half the physical cost of the DCC. The simulation results show the MCC has slight higher than the DCC for the restoration time and non-restoration ratio, however, the MCC has better cost-efficiency than the DCC for USANET and Icosahedrons networks.