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Today, the Web is a place for offering single services and developing service compositions. Increasing number of service providers has introduced the challenge of QoS-aware selection of web service compositions. In such compositions, appropriate web services are selected among several function-equivalent available services. This selection is performed in such a way that the resulting composite web service has optimal quality and satisfies user's quality requirements. In this paper, the problem of QoS-aware selection of web service composition is modeled as an optimization problem. Then a variation of Harmony Search algorithm is used to find a near-optimal composition which can satisfy local and global user's constraints on quality attributes. Compared with other approaches, the proposed method works faster and more accurately.