The quality of a product is one of the major interests of the manufacturing process in all industries. The software industry imposes to construct a project with several phases to ensure producing high-quality software. A software development company estimates time, effort and cost of the project during planning phase. It is important to have accurate estimations to reduce the risks of project failure. Several cost estimation methods are practiced in the software development companies such as Function Point (FP), Use Case Points (UCP), Constructive Cost Model I and II and Story Points (SP). UCP cost estimation method is taken in this research to improve the accuracy of its estimation. UCP estimation depends on the use case diagram of the proposed system. A use case diagram describes the main functional requirements of the proposed system. UCP partially considers non-functional requirements through the technical and environmental factors. There is a lacking in the UCP method to consider the importance of quality attributes in the estimating process. This paper proposes an extended version of the existing UCP method named Quality Extended Use Case Point (QUCP) method in which quality attributes are included to improve the accuracy of cost estimation. A questionnaire is used to validate the proposed QUCP method. It is found after data analysis that seventy five percentages of the participants are agreed that the proposed method will not only help to improve the accuracy of cost estimation but it will also enable a software development company to deliver high-quality products.