In cognitive radio networks, cooperative spectrum sensing (CSS) is a key approach to effectively discover spectrum opportunities for secondary users. However, due to the presence of malicious nodes, CSS faces significant challenges in the trust issue of sensing results caused by spectrum sensing data falsification and the privacy leakage of sensing nodes. In this article, we develop a trustworthy and privacy-preserving CSS solution based on blockchain, TaP2-CSS. It achieves the transparency and trustworthiness in exchanging and fusing sensing reports and preserves privacy of sensing nodes. More specifically, a fusion scheme is proposed to realize the high defense capability against the spectrum sensing falsification attack launched by lurking and persistent malicious nodes. Furthermore, to address privacy threats of sensing nodes, we propose a privacy-preserving sensing scheme based on dynamic sensing time for resource-constrained sensing nodes. It effectively limits the location information leaked by sensing reports without the need for complex cryptographic computation and protocol interaction. Comprehensive evaluation and comparison show that the proposed solution achieves high sensing accuracy in the presence of malicious nodes while preserving the privacy of sensing nodes.