In order to obtain better performance at low SNR regimes and reduce computational complexity in wideband sensing, a novel cyclostationary spectrum sensing (CSS) algorithm exploiting partial QR decomposition is proposed in this paper. At the first step of the CSS algorithm, spectral correlation functions (SCFs) for sampled signals that exhibit cyclostationary are calculated by secondary user (SU) to get an SCFs matrix, and then the SCFs matrix is rotated at an appropriate angle. After that, partial QR decomposition for some major components of the SCFs matrix is performed to sense the presence of the primary users (PUs). The feature that noise components is only related to floor noise makes the proposed CSS algorithm more efficient than energy detections, especially at low SNR regimes. And compared with traditional cyclostationary methods, partial QR decomposition for only some major components can reduce computational complexity largely when the sensing band is wide. Simulation results show that the proposed CSS algorithm performs much better than the traditional ones in terms of false-alarm probabilities, detection probabilities, and computational complexity, such as MAJ-OC based, ML-OC based CSS algorithms. Besides, the proposed CSS algorithm is robust, which can be used for various kinds of modulated signals, such as OFDM, QPSK, MSK, and 16QAM.