The ability to accurately predict future resource capabilities is of great importance for applications and scheduling algorithms which need to determine how to use time-shared resources in a dynamic grid environment. In this paper we present and evaluate a new and innovative method to predict the one-stepahead CPU load in a grid. Our prediction strategy forecasts the future CPU load based on the tendency in several past steps and in previous similar patterns, and uses a polynomial fitting method. Our experimental results demonstrate that this new prediction strategy achieves average prediction errors that are between 37% and 86% lower than those incurred by the previously best tendency-based method.