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Spectrum sensing method for cognitive wireless cloud computing (CWC) network is very challenging since there are several different communication systems should be detected at very low SNR (as low as -22 dB). In this paper, we propose a kurtosis based spectrum sensing method which can be applied efficiently in such environment. The proposed method uses kurtosis estimation of received samples. Its value will be equal or close to 3 when only gaussian noise samples exist in the received signal. This kurtosis estimation's used to distinguish between the present or absent of primary signal by comparing with a predefined threshold. Simulation's done to evaluate its performance. Results show that the proposed method performs much better than energy detection especially at low SNR, even below -20 dB. It also gives benefit in much simple implementation for CWC network since it doesn't need knowledge of primary signal's parameters.