Cloud computing web services are the most current and improving technology. In this paper we have two-factor authentication access control system for cloud computing services based on web. In our proposed two factor authentication control system, an attribute-based access control mechanism is implemented with the necessity of a user secret key and an OTP (One Time Password). A user can access the system only if they hold the two factors as mentioned above, this solution can improve the security of the system specifically in times of problem where many users share the same computer for web-based cloud services. Because we are using attribute-based authentication control which is one of our important factor in the system that enables the cloud server to restrict the access to those users with the same set of attributes while preserving user privacy. We use the most improvised algorithm which is a combination of ABE (Attribute Based Encryption) and ABC (Attribute Based Credentials) called ABKE (Attribute Based Key Exchange) which is provided by a certificate authority. We test our system and see the practicability of our proposed three factor authentication system.