Abstract: With the help of futures hedging, the business can avoid or minimize spot price risks. But people often find the ratios of hedging by least variance method and its risks. In this paper, we analysis the defects of least variance method, and advance a least second moment method of the futures hedging. We get new hedging ratios, total risk of hedging, short hedging risk and long hedging risk. The theory basis is provided for that we judge the present price to fit short hedging or long hedging.