Cloud computing in a narrow sense is technically different from the traditional server-client model, grid computing, etc., the systems architecture of the software systems involved in the delivery of cloud computing, typically involves multiple cloud components communicating with each other over application programming interfaces, usually web services. Conceptually speaking, there isn't that much difference with other server-server-client models. Cloud computing is an Internet-based computing service provided by the third party allowing share of resources and data among devices. It is widely used in many organizations nowadays and becoming more popular because it changes the way of how the Information Technology (IT) of an organization is organized and managed. While there is increasing use of cloud computing service in this new era, the security issues of the cloud computing become a challenges. This paper firstly lists out the architecture of the cloud computing, then discuss the most common security issues of using cloud and some solutions to the security issues since security is one of the most critical aspect in cloud computing due to the sensitivity of userís data.