The existing Goodness of fit (GoF) test based spectrum sensing algorithms mostly use samples or energies as observations to make decisions, which can hardly achieve satisfactory performance especially when the Primary user (PU) signals are highly correlated. Meanwhile, the eigenvalue of covariance matrix can reflect signal correlations well. Motivated by this, we study the distribution of eigenvalue and propose an eigenvalue based GoF spectrum sensing algorithm. In the proposed scheme, we use the ratios of maximum to minimum eigenvalue as observations and thus it can bring performance improvements through capturing correlation of PU signals. We also provide the related theoretical analysis for the proposed method. Simulation results show that the proposed method overcomes the problem of noise uncertainty and achieves performance improvement over the classical samples-based GoF test.