Crowdsensing is a participatory sensing service where a server analyzes sensing data gathered from multiple users' devices. In crowdsensing, user's anonymity is desired, since the server collects their sensitive data including GPS locations and moving path. However, the anonymous submission may compromise the sensing data trust, because users may submit inappropriate data without being traced. Therefore, ARTSense (Oscar et al., Infocom 2013) has been proposed to achieve both anonymity and trust in crowdsensing. The trust of sensing data is assessed from the sensed environment, similarity check, and user reputation, which is anonymously managed on the feedback of the data trust assessment. However, in ARTSense, the user needs to wait a random time after the submission phase before requesting the reputation update, which causes communication delay. Hence, an efficient anonymous reputation system for crowdsensing is proposed to be integrated with the trust assessment of ARTSense. In the proposed system, the reputation update is anonymously completed because each user manages his/her reputation on the user side instead of the server. The validity of the reputation is ensured by a certificate and anonymously checked by zero-knowledge proofs. As a result, communication rounds are also reduced. Therefore, the proposed system achieves better efficiency without delay.