In this paper، we propose a new algorithm of spectrum sensing based on algorithmic information theory. Since the proposed algorithm is applied in time domain، resulting in an overall reduction on the system computational complexity. In this paper، we investigate two cases of wideband and narrowband spectrum sensing problems. To sense the spectrum، we propose to use some measures based on algorithmic information theory such as Lempel-Ziv Complexity (LZC)، Higuchi fractal dimension (HFD)، and Algorithmic mutual information (algorithmic MI). LZC and HFD are reliable and promising measures that calculate the complexity of a time series signal in a straight forward manner. On the other hand، algorithmic MI calculates the algorithmic mutual information between two time series signals. Our proposed algorithm is blind in the sense that it requires no prior knowledge of the channel، primary users’ signals، and noise variance. In simulation section، it is shown that our proposed algorithm has better performance in contrast with the other complexity based detectors such as Shannon entropy and spectral entropy based detectors.