The dissertation presents a new parallel programming paradigm for developing high performance (HPC) applications on the Grid. We address the question "How to tailor HPC applications to the Grid?" where the heterogeneity and the large scale of resources are the two main issues. We respond to the question at two different levels: the programming tool level and the parallelization concept level. At the programming tool level, the adaptation of applications to the Grid environment consists of two forms: either the application components should somehow decompose dynamically based on the available resources; or the components should be able to ask the infrastructure to select automatically the suitable resources by providing descriptive information about the resource requirements. These two forms of adaptation lead to the parallel object model on which resource requirements are integrated into shareable distributed objects under the form of object descriptions. We develop a tool called ParoC++ that implements the parallel object model. ParoC++ provides a comprehensive object-oriented infrastructure for developing and integrating HPC applications, for managing the Grid environment and for executing applications on the Grid. At the parallelization concept level, we investigate the parallelization scheme which provides the user a method to express the parallelism to satisfy the user specified time constraints for a class of problems with known (or well-estimated) complexities on the Grid. The parallelization scheme is constructed on the following two principal elements: the decomposition tree which represents the multi-level decomposition and the decomposition dependency graph which defines the partial order of execution within each decomposition. Through the scheme, the parallelism grain will be automatically chosen based on the available resources at run-time. The parallelization scheme framework has been implemented using the ParoC++. This framework provides a high level abstraction which hides all of the complexities of the Grid environment so that users can focus on the "logic" of their problems. The dissertation has been accompanied with a series of benchmarks and two real life applications from image analysis for real-time textile manufacturing and from snow simulation and avalanche warning. The results show the effectiveness of ParoC++ on developing high performance computing applications and in particular for solving the time constraint problems on the Grid.