Web service is a software application, which is accessible using platform independent and language neutral web protocols. However, selecting the most relevant services became one of the vital challenges. Quality of services plays very important role in web service selection, as it determines the quality and usability of a service, including its non-functional properties such as scalability, accessibility, integrity, efficiency, etc. When agent application send request with a set of quality attributes, it becomes challenging to find out the best service for satisfying maximum quality requirements. Among the existing approaches, the single value decomposition technique is popular one; however, it suffers for computational complexity. To overcome this limitation, this paper proposed a subset matching based web service selection and ranking by considering the quality of service attributes. This proposed method creates a quality-web matrix to store available web services and associated quality of service attributes. Then, matrix subsets are created using web service repository and requested quality attributes. Finally, web services are efficiently selected and ranked based on calculated weights of corresponding web services to reduce composition time. Experimental results showed that proposed method performs more efficient and scalable than existing several techniques such as single value decomposition.