Among the existing spectrum sensing algorithms, energy detection can be implemented easily, but its detection performance depends on noise power. Spectrum sensing algorithms based on random matrix theory can skillfully avoid the influence of noise uncertainty on detection performance, but most of them make use of approximate distribution of the largest eigenvalue. The accuracy of threshold expression derived from it needs to be further improved. Aiming to above problems, by using the latest research results about random matrix theory, a spectrum sensing algorithm based on distribution of the least eigenvalue of sample covariance matrix of received signals was proposed. Cumulative distribution function of the least eigenvalue is not based on asymptotical assumptions, which is more suitable for realistic communication scenarios. The threshold expression derived from it was a function of false alarm probability, whose effectiveness and superiority were analyzed and verified with few samples. Simulations complied with single variable principle were conducted under the situation of few samples, few collaborative users, low signal to noise ratio and low false alarm probability, in comparison with classic maximum-minimum eigenvalue algorithm. Detection probability of the proposed algorithm was increased by 0.2 or so. The results show that the proposed algorithm can significantly improve the detection performance of system.