Global computing system (GCS) harnesses the idle CPU resources of clients connected to Internet for solving large problems that require high volume of computing power. Since GCS scale to millions of clients, many projects usually adopt coarse-grained scheduling in order to reduce server-side contention at the expense of sacrificing the degree of parallelism and wasting CPU resources. In this paper, we propose a new type of client, i.e., a scheduling proxy that enables adaptive-grained scheduling between the server and clients. While the server allocates coarse-grained work units to scheduling proxies alone, clients download fine-grained work units from a relatively nearby scheduling proxy not from the distant server. By computation of small work units at client side, the turnaround time of work unit can be reduced and the waste of CPU time by timeout can be minimized without increasing the performance cost of contention at the server. In addition, in order not to lose results in the failure of scheduling proxies, we suggest a technique of result caching in clients.