Spectrum sensing is a key technical challenge for cognitive radio (CR). It is well known that multi-cycle cyclostationarity (MC) detector is a powerful method for spectrum sensing. However, conventional MC detector is difficult to implement due to its high computational complexity. This paper pays attention to the fact that the computation complexity can be reduced by simplifying the test statistic of conventional MC detector. Based on this simplification process, an improved MC detector is proposed. Compared with the conventional one, the proposed detector has the low-computational complexity and sufficient-accuracy on sensing performance. Subsequently, the sensing performances are further investigated for the cases of Rayleigh, Nakagami-m, Rician, composite Rayleigh fading-lognormal shadowing and composite Nakagami fading-lognormal shadowing channels, respectively. Furthermore, the square-law combining (SLC) is introduced to improve the detection capability over fading-shadowing channels. The corresponding closed-form expressions of average detection probability are derived for each case by the moment generation function (MGF) approach. Finally, illustrative and analytical results show that the efficiency and reliability of proposed detector and the improvement on sensing performance by SLC over composite fading-shadowing channels.