This paper presents a new cyclic direction-of-arrival (DOA) estimation algorithm. By exploiting a new minimum-redundancy linear-array (MRLA) configuration and cyclostationarity, the proposed algorithm computes a covariance matrix of the MUSIC method with a pseudo-data matrix of 2N-1 virtual sensors, which are the results of temporal and spatial processing with the designed M-sensor Sum-MRLA. Theoretical analysis and computer simulations show that, for each cyclic frequency, the algorithm can estimate 2N-2 DOAs with M-sensor Sum-MRLA (N>M).