The purpose of this paper is to demonstrate the design and implementation of GISolve - a Grid-based problem solving environment for computationally intensive geographic information analysis based on geo-middleware. The geo-middleware resides between existing Grid middleware and geographic information analysis applications to manage heterogeneous and dynamic resources on behalf of analysis applications. At the same time, GISolve provides adaptive domain decomposition solutions to parallel geographic information analysis applications. Based on these domain decomposition solutions, GISolve also schedules distributed tasks and manages data transfers. In GISolve, these capabilities are designed as Grid services that are compliant with the open Grid service architecture (OGSA) and are implemented using Grid portal technologies. The GISolve implementation is illustrated based on a case study of a computationally intensive spatial statistic - [G i(d)] that is used to assess spatial dependence among geographically distributional observations.