The two-tiered wireless sensor networks have become the research hotspot because of its scalability and long lifetime. Top-k query is an important query type but most Top-k query technologies cannot perform precise query. A Top-k query asks for data items whose numeric attributes are among the k highest, where k is an application-dependent parameter. The privacy preservation is important for Top-k query in a hostile environment because sensitive information may leak from compromised nodes. The integrity and authenticity of the Top-k query results should be verified because the adversary can instruct a compromised master node to delete or modify data in response to Top-k queries. This paper presents a precise query algorithm called PI-TQ (privacy-preserving integrity-verification Top-k query) which provides both privacy preservation and integrity verification. The algorithm uses a two-step query method to reduce the communication traffic between nodes and sinks. To ensure the privacy and correctness of the query results, the perturbation algorithm is utilized to protect the privacy of sensitive data. The neighbor verification method achieves integrity verification by using probability space. The simulation results show that PI-TQ algorithm can greatly reduce the computational cost and traffic consumption compared with other algorithms. It can also guarantee accuracy, privacy and integrity of the query results.