Web APIs provide enterprises with a new way of driving innovations of new technology with limited resources. API recommendations greatly alleviate the selection burdens of enterprises in identifying potential useful APIs to meet their business demands. However, these approaches disregard the privacy leakage risk in cross-platform collaboration and the popularity bias in recommendation. To address these issues, first, we introduce MinHash, an instance of locality-sensitive hashing, into a collaborative filtering technique and propose a novel, privacy-enhanced, API recommendation approach. Second, we present a simulation algorithm to analyze the popularity bias in API recommendation. Third, we mitigate popularity bias by improving the novelty of recommendation results with an adaptive reweighting mechanism. Last, comprehensive experiments are conducted on a real-world dataset collected from ProgrammableWeb. Experimental results show that our proposed approach can effectively preserve usage data privacy and mitigate popularity bias at a minimum cost in accuracy.