Web services are a technology that has been growing rapidly since its inception earlier this century. They are so popular nowadays that they are being used for numerous purposes, spanning business, healthcare, education and government applications. They are used for accessing diverse types of data in domains such The financial, climate forecasting and sports, among others. As a result of this increased popularity, it is very common to find a large number of applications providing exactly the same service. Having a large number of applications to choose from, one that integrates a selection mechanism using quality criteria for selecting the best choice, has an advantage over other applications that do not provide this feature. However, the selection of the best Web service, among various services with the same functionality, is not an easy task. Therefore, the design of a worthwhile technique to determine the best Web service by assessing its quality of service is important. Hidden Markov models are probabilistic methods that allow us to build behavior models of the Web services. Such models can be used to predict their behavior in the near future. In this paper, we propose a method for selecting Web services based on the response time QoS parameter and hidden Markov models.