GM(1, 1) is an effective tool for manipulating data sequence that include only poor information, which is a basic model of grey theory system and used widely. The effectiveness and presupposition of GM(1, 1) are analyzed from a new aspect by the residual function. The result indicates that GM(1, 1) leads to a good simulation work only when sample number closes to infinity on the index decay sequence, and the distribution of residual is not balanced on various data points and commonly becomes bigger more and more when sample points close to infinity.