Aiming at the problems of inadequate accuracy in the prediction of multi-chip module life using traditional gray model and the significant decrease in prediction accuracy with the increase of time span, a Markov-tail double residual correction method for multi-chip component life prediction based on grey model is proposed. Based on the predicted value of grey GM ( 1,1) model, the residual optimized by Markov method is used as the input value of the tail segment grey residual model to achieve double residual correction. An example is given to predict the life of multi-chip module by using resistance values which influence the life of multi-chip module with a small amount of test data obtained under the condition of accelerated thermal cycle test. The experimental results show that compared with the traditional grey model and neural network prediction methods, the average residuals of the proposed method are reduced by 80. 469% and 68. 53% under the small samples condition, the prediction accuracy is improved, the result is more reliable and the life prediction of multi-chip modules can be more accurate.