Abstract: The problem of scarcity of spectrum resources is becoming one of the hot issues. To overcome the problem of spectrum crisis, cognitive radio was proposed as an important technology. Spectrum sensing algorithm based on goodness of fit (GoF) test is an excellent perceptual algorithm, which can achieve good detection performance under small number of samples without any information of the primary users (PUs). The existing spectrum sensing algorithms based on GoF test indeed present excellent performance under static signals, but it degrades sharply when detecting dynamic signal. Aiming at this problem, this paper presents a GoF detection algorithm based on maximum eigenvalue. The new algorithm utilizes random matrix theory to analyze distribution of the maximum eigenvalue of sample covariance matrix and detects the existence of main users by GoF test, which can still present good detection performance under dynamic signals. In addition, a low-complexity fitting criterion is designed for the proposed detection method, which is able to improve the detection performance with a low computational complexity of fitting statistics of GoF algorithms. Simulation results show the efficiency of the proposed fitting criterion and detection algorithm.