On the basis of introducing the fundamental principles of the least square methods, the Chebyshev polynomial data fitting method is given, by using this method, the grain yield of Jilin Province from 1952 to 2008 is analyzed. The results show that when analyzing the research data of agricultural economy, the least square method of the Chebyshev polynomials is a good choice; by establishing the prediction model of the least square method of Chebyshev polynomials, we get the results that the grain yield in Jilin Province from 2009 to 2015 is 29.004 millon, 29.836 million, 30.681 million, 31.540 million, 32.412 million, 33.298 million, 34.197 million ton ; the annual average growth rate of grain yield from 2009 to 2015 is 2.78%, lower than the annual growth rate of 7.12% from 2000 to 2008.
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