Spectrum sensing algorithm based on fractional wavelet transform was proposed to solve the problem that the performance of non-stationary signal energy detection was not satisfactory in low SNR scenarios .Firstly, the fractional wavelet transform is made for the received signal to gather the energy and undermine the noise,then the energy detection is done to the reconstructed signal. Both the theory analysis and the simulation results show that this algorithm could improve the performance of non-stationary signal energy detection in low SNR scenarios.When the sensing rate is 0.3, spectrum sensing algorithm based on fractional wavelet transform gets 6dB and 2dB SNR gain compared with the traditional algorithm and algorithm based on wavelet transform; In the condition that the constant false alarm rate is 0.1,the sensing rate of spectrum sensing algorithm based on fractional wavelet transform is 0.867,which is obviously higher than the 0.287 of traditional algorithm and the 0.628 of algorithm based on wavelet transform.