Interoperability between different Grid implementations is attracting more and more attention to seamlessly job execution. In this paper, one approach is proposed to implement the basic interoperability between heterogeneous Grids based abstractions provided by ChinaGrid Support Platform (CGSP). The minimal set of service and functionalities required by seamlessly job execution racted first. Then the problems encountered and corresponding solutions taken within integrating CGSP with other OGSA-compliant Grids are described, and the specific interoperability issues including job submission and job execution management, data management and staging, resource representation and discovery, security and identities management are addressed as well. At last, GPE4CGSP, which integrates CGSP with Grid Programming Environment (GPE), is given as a case study to verify the feasibility of the approach.