The medium-and-long-term prediction of precipitation is not only difficult in meteorology,but also an important issue in hydrology. The logarithmic Markov chain model is established to predict precipitation, which can compensate the uncertainty of peak point in precipitation prediction by the traditional Markov mod-el and raise the prediction accuracy. At last,precipitation data of 43 years from the hydrological station in Yanchi County are used to verify the model,and prediction accuracy is found to be satisfied. So,the loga-rithmic Markov chain can provide an oversimplified channel to the medium-and-long-term precipitation predic-tion in the semi-arid sandy region.