Computational grids present promising computational and storage capacities. They can be made by punctual aggregation of smaller resources (i.e., clusters) to obtain a large-scale supercomputer. Running general applications is challenging for several reasons. The first one is inter-process communication: processes running on different clusters must be able to communicate with one another in spite of security equipments such as firewalls and NATs. Another problem raised by grids for communication-intensive parallel application is caused by the heterogeneity of the available networks that interconnect processes with one another. In this paper we present how QCG-OMPI can execute efficient parallel applications on computational grids. We first present an MPI programmation, communication and execution middleware called QCG-OMPI. We then present how applications can make use of the capabilities of QCG-OMPI by presented two typical, parallel applications: a geophysics application combining collective operations and a master-worker scheme, and a linear algebra application