Iterative multiple imputation is a popular technique for missing data analysis. It updates the parameter estimators iteratively using multiple imputation method. This technique is convenient and flexible. However, the parameter estimators do not converge point-wise and are not efficient for finite imputation size m. In this paper, we propose a regression multiple imputation method. It uses the parameter estimators obtained from multiple imputation method to estimate the parameter estimators based on expectation maximization algorithm. We show that the resulting estimators are asymptotically efficient and converge point-wise for small m values, when the iteration k of the iterative multiple imputation goes to infinity. We evaluate the performance of the new proposed methods through simulation studies. A real data analysis is also conducted to illustrate the new method.