Algorithms based on signal correlation have low computational complexity and require little knowledge on primary signals or noise signals. However, their detection performance becomes relatively terrible in low signal-to-noise ratio (SNR) regime with weak signal correlation, which happens to be quite common in practical systems. In this paper, a weighted blind spectrum sensing algorithm based on signal correlation is proposed to effectively improve the detection performance on the basis of above-mentioned advantages of correlation- based detection. This proposed algorithm adequately exploits the auto-correlation (AC) and cross-correlation (CC) characteristics of received signals and assigns a proper weighting coefficient to each term in the test statistic of our algorithm, enlarging the difference of test statistic with or without the existence of primary users (PUs) and thus greatly promoting the detection performance. False alarm and detection probabilities are analyzed thoroughly in the low-SNR regime, and their approximate analytical expressions are derived based on the central limit theorem (CLT). Simulations are presented to verify the analyses. Experiments show that the proposed detection can significantly outperform other correlation-based algorithms.