Grid brings the power of many computers to scientists. However, the development of Grid-enabled applications requires knowledge about Grid infrastructure and low-level API to Grid services. In turn, workflow management systems provide a high-level environment for rapid prototyping of experimental computing systems. Coupling Grid and workflow paradigms is important for the scientific community: it makes the power of the Grid easily available to the end user. The paradigm of data driven workflow execution is one of the ways to enable distributed workflow on the Grid. The work presented in this paper is carried out in the context of the Virtual Laboratory for e-Science project. We present the VLAM-G workflow management system and its core component: the Run-Time System (RTS). The RTS is a dataflow driven workflow engine which utilizes Grid resources, hiding the complexity of the Grid from a scientist. Special attention is paid to the concept of dataflow and direct data streaming between distributed workflow components. We present the architecture and components of the RTS, describe the features of VLAM-G workflow execution, and evaluate the system by performance measurements and a real life use case.