This paper presents our first-step efforts towards agent based computing grid on the Web. When there are several prototypes addressing volunteer computing, our model is actually the one that focuses on open issues in them, i.e., Adaptive Parallelism, Scalability, Applicability and FaultTolerance. The motivation of our work is from the growing consensus that socially intelligent agents naturally model complex systems in an uncertain and changing environment. For being applicable to the real Web environment, in the design of our model, we do not limit the number of volunteers or clients; we do not require volunteers' persistence; we support fine-grained applications and tolerate potential crash of volunteer machines. Based on ideas of this paper, we have set up a project, and the first version of the prototype system, called Supagents 1.0, has been developed. So far, some of the claimed features of our model have been demonstrated by dedicatedly designed benchmark applications.