It is proved that cloud computing has many benefits, and cloud services with flexible licensing model and cost saving features bring opportunities to enterprise's IT operations. Conventional ERP system, an important component of enterprises, is impacted by on-demand cloud services also. Integrating conventional ERP system with cloud services becomes a trend because it brings new processing capabilities without introducing significant changes to existing system. But previous studies about integrating ERP and cloud usually focused on SaaS (Software as a Service). PaaS (Platform as a Service) and IaaS (Infrastructure as a Service) are not discussed much. People sometimes even confuse cloud service with SaaS. Therefore, the objective of this paper is to present a framework that can describe respective implications of integrating ERP with three types of cloud services: SaaS, PaaS and IaaS. Qualitative methods such as systematic literature review and interviews are adopted to execute the research, so data collected through different sources can complement each other in order to support presenting the framework of integrating conventional ERP system and cloud services. The integration at SaaS level is for achieving immediate business value and productivity enhancement. At PaaS level the objective of integration is to enhance software development life cycle management. And the main integrating intent at IaaS level is to enable scalability and reliability of hardware resources without changing existing IT infrastructure. Furthermore, challenges and opportunities for integrating ERP with different cloud services are studied and motivation is derived from analyzing. Finally the key points are arranged in the presented framework of integration between conventional ERP systems and cloud services.