Abstract: Abstract: The relations between China's grain yield and some main factors influencing the grain yield, more present the exponential function and few exponent sign function relations. To describe with a new type of exponential production function can obtain a better result because of less error. The paper pointed out that the least absolute deviations (LAD) method, as its excellent properties, may be a best method to find the"implicit function"which is behind the data and control the data. To knead the two together, with the LAD method to fit the exponential production function, trying to find out some rules for China's grain change is a subject that is worth of exploring in theory and application. The paper introduces the LAD method and the exponential production function, establishes correlations between the China's grain yield and its 5 major influencing factors (consumption of chemical fertilizer, total sown area, total area affected by natural disaster, total agricultural machinery power, and total employed persons of primary industry). The production function model was fit with the LAD method, and the data of 1983-2011 were calculated. The results with Mae (mean absolute error) not over 3.93 million tons and Mape (mean absolute percentage error) not more than 0.87% for China's grain yield during the 29 years were obtained, and the conclusions were explained and analyzed; The analysis showed that, in the 29 years of 1983-2011, the growth of China's nation grain yield mainly depended on the consumption of chemical fertilizer and the total agricultural machinery power, of which the consumption of chemical fertilizer is still playing a positive roll up to now, while the total agricultural machinery power is dynamically in a saturated state. Theoretically it should have a "negative" effect now, but in reality it does not. The total sown area was the most influencing "positive" factor. The national grain yield may still grow further without increasing the total sown area, but increasing the sown area can rapidly boost the China's nation grain yield. The total area affected by natural disaster imposed "negative" effect on the growth; However, the trend of its influence is increasing in terms of absolute values, but is decreasing in terms of relative values. By the huge impact and lagged effects of the rapid growing of the total employed population of primary industry in China during 1983-1993 period, the reduction of the total employed population of primary industry to grain growth constituted "negative" impact. With the modernization of agriculture and urbanization development, this "negative" impact continued to reduce. These conclusions give the specific quantitative values. The paper predictes that the grain yield for year 2012 is t, the later result indicates the absolute error is t, and the relative error is 0.3%. For year 2013, the prediction is t. In the last the paper gives some discussion about the LAD method, the exponential production functions and so on, and is concluded that the exponential production function under the meaning of LAD criterion to describe the relationships between China's grain yield and the main effect factors, has a certain accuracy and guiding sense.