There have been proposed several dynamic load-balancing methods for web server clusters. In order to realize an effective load-balancing, they have required an almost real-time server load information which could be obtained from an observation of client-server interactions or a frequent polling from the load-balancer (dispatcher) to each server. However the observation provides an indirect server load information and the polling interval produces a time-lag. To overcome that problem, this paper proposes a load-balancing method based on a server load estimation. Under an employment of our method, the load-balancer selects an estimated least-loaded server, and then assigns the arriving request to that server. The estimation is based on a fact that the file transfer delay is proportional to the file size. The fact makes it possible to estimate each server load from the last request assigned time and the file size. From a performance comparison with the previously proposed methods, our method can realize an effective load balancing for web server clusters.