The increasing momentum of service-oriented architecture has led to the emergence of divergent delivered services, where service selection is meritedly required to obtain the target service fulfilling the requirements from both users and service providers. Despite many existing works have extensively handled the issue of service selection, it remains an open question in the case where requests from multiple users are performed simultaneously by a certain set of shared candidate services. Meanwhile, there exist some constraints enforced on the context of service selection, e.g. service placement location and contracts between users and service providers. In this paper, we focus on the QoS-aware service selection with constraints from a fairness aspect, with the objective of achieving max-min fairness across multiple service requests sharing candidate service sets. To be more specific, we study the problem of fairly selecting services from shared candidate sets while service providers are self-motivated to offer better services with higher QoS values. We formulate this problem as a lexicographical maximization problem, which is far from trivial to deal with practically due to its inherently multi-objective and discrete nature. A fairness-aware algorithm for concurrent service selection (FASS) is proposed, whose basic idea is to iteratively solve the single-objective subproblems by transforming them into linear programming problems. Experimental results based on real-world datasets also validate the effectiveness and practicality of our proposed approach.