Cooperative (spectrum) sensing is a key function for dynamic spectrum access and is essential for avoiding interference with licensed primary users and identifying spectrum holes. A promising approach for effective cooperative sensing over a large geographic region is to rely on special spectrum-sensing providers (SSPs), which outsource spectrum-sensing tasks to distributed mobile users. Its feasibility is deeply rooted in the ubiquitous penetration of mobile devices into everyday life. Crowdsourcing-based cooperative spectrum sensing is, however, vulnerable to malicious sensing data injection attack, in which a malicious CR users submit false sensing reports containing power measurements much larger (or smaller) than the true value to inflate (or deflate) the final average, in which case the SSP may falsely determine that the channel is busy (or vacant). In this paper, we propose a novel scheme to enable secure crowdsourcing-based cooperative spectrum sensing by jointly considering the instantaneous trustworthiness of mobile detectors in combination with their reputation scores during data fusion. Our scheme can enable robust cooperative sensing even if the malicious CR users are the majority. The efficacy and efficiency of our scheme have been confirmed by extensive simulation studies.