Cloud computing is a Technology that has come out in the last decade and that is transforming the IT industry in huge. The Cloud computing is playing a vital role as a backbone component of the Internet of Things (IoT). In a Cloud Computing scenario, cloud services are accessible via Internet. Cloud computing is providing ondemand resources like Infrastructure, platform, and software as it is do not pay to possess the software itself but rather to use it. Pay for use concept is very attractive, hence many organizations are adopting the SaaS model drastically. Even though, each customer is unique and leads to unique variation in the requirements of the software. the SaaS is generally press into service and it yields advantages to service providers and service customers. More and more SaaS services are emerging, how to select qualified service is key problem for customers. Present quality models are not sufficient to evaluate SaaS selection on the cloud due to its tremendous increasing in the use. A quality model can be used to represent, evaluate, and differentiate the quality of the SaaS providers. In this paper, a new quality model proposed and named SAASQUAL for cloud software services.This model is based on different attributes of quality software, quality service and metrics that measure software quality and service quality in order to evaluate potential software as a service on the cloud.