Missing data are common in data analyses in biomedical fields, and imputation methods based on random forests (RF) have become widely accepted, as the RF algorithm can achieve high accuracy without the need for specification of data distributions or relationships. However, the predictions from RF do not contain information about prediction uncertainty, which was unacceptable for multiple imputation. Available RF-based multiple imputation methods tried to do proper multiple imputation either by sampling directly from observations under predicting nodes without accounting for the prediction error or by making normality assumption about the prediction error distribution. In this study, a novel RF-based multiple imputation method was proposed by constructing conditional distributions the empirical distribution of out-of-bag prediction errors. The proposed method was compared with previous method with parametric assumptions about RF's prediction errors and predictive mean matching based on simulation studies on data with presence of interaction term. The proposed non-parametric method can deliver valid multiple imputation results. The accompanying R package for this study is publicly available.