In the last couple of years, Cloud computing has evolved as an important paradigm for IT industry with reduced costs, payas-you-use, scalability, easy accessibility and improved flexibility. More and more small and large scale companies are moving towards cloud computing as it eliminates setting up of high-investment on IT infrastructure and other services like SaaS, Paas and NaaS. In cloud environment, the client data can reside in any corner of the world and maintained and controlled outside their reach. So, there can be security and privacy issues with the client data. The cloud provider needs to satisfy their client by ensuring and providing data security.This survey paper presents and analyze different security and privacy issues involved in cloud computing service. We also highlight different security models of few of the top cloud service providers. This research paper introduces new service model called Data Outsourcing Security as a Service (DOSaaS).