The population growth reaches one hundred million in the world and twenty million in China every year. The prospect of mankind is clousely togetber with food production and so is the arable land change.How to tackle the relationship of population-food-arable land should be an imporrant problem in face of the world. This paper applying the central link formulae and gray system in population-food-arable land relationship does an analysis of population growth and food production of Guyuan County for 9 years in the past and 12 years in the future refering to some countries in the world, and it was done under different rates controlling population growth.The conclusion is that if it is going on as the current rates of population growth and food production to the end of the contury, the food shortage for Guyuan County will be very serious, and it is only controlling population growth strictly, and increassing agricultural input energetically the state in the future may be better.