Mobile Crowdsourcing (MCS) has become a novel paradigm for enabling data collection by worker recruitment, and the reputation plays a crucial role in achieving high-quality data. Although identity, data, and bid privacy preserving have been thoroughly investigated with the advance of blockchain technology, existing literature barely focuses on reputation privacy, which prevents malicious workers from submitting false data that could affect truth discovery for data requester. Therefore, we propose a Blockchain-Based Reputation Privacy Preserving for Quality-Aware Worker Recruitment Scheme (BRPP-QWR). First, we design a lightweight privacy preserving scheme for the whole life cycle of the worker’s reputation, which adopts sub-address retrieval technique combined with Pedersen Commitment and Compact Linkable Spontaneous Anonymous Group (CLSAG) signature to enable fast and anonymous verification of the reputation update process. Subsequently, to tackle the unknown worker recruitment problem, we propose a Reputation, Selfishness, and Quality-based Multi-Armed Bandit (RSQ-MAB) learning algorithm to select reliable and high-quality workers. Lastly, we implement a prototype system on Hyperledger Fabric to evaluate the performance of the reputation management scheme. The results indicate that the execution latency for the reputation score verification and retrieval latency can be reduced by an average of 6.30%–56.90% compared with ARMS-MCS. In addition, experimental results on both real and synthetic datasets show that the proposed RSQ-MAB algorithm achieves an increase of at least 20.05% in regard to the data requester’s total revenue and a decrease of at least 48.55% and 3.18% in regret and Multi-round Average Error (MAE), respectively, compared with other benchmark methods.