In cognitive radio networks, cooperative spectrum sensing (CSS) has been a promising approach to improve sensing performance by utilizing spatial diversity of participating secondary users (SUs). In current CSS networks, all cooperative SUs are assumed to be honest and genuine. However, the presence of malicious users sending out dishonest data can severely degrade the performance of CSS networks. In this paper, a framework with high detection accuracy and low costs of data acquisition at SUs is developed, with the purpose of mitigating the influences of malicious users. More specifically, a low-rank matrix completion based malicious user detection framework is proposed. In the proposed framework, in order to avoid requiring any prior information about the CSS network, a rank estimation algorithm and an estimation strategy for the number of corrupted channels are proposed. Numerical results show that the proposed malicious user detection framework achieves high detection accuracy with lower data acquisition costs in comparison with the conventional approach. After being validated by simulations, the proposed malicious user detection framework is tested on the real-world signals over TV white space spectrum.