Missing values are a practical issue in the analysis of longitudinal data. Multiple imputation (MI) is a well-known likelihood-based method that has optimal properties in terms of efficiency and consistency if the imputation model is correctly specified. Doubly robust (DR) weighing-based methods protect against misspecification bias if one of the models, but not necessarily both, for the data or the mechanism leading to missing data is correct. We propose a new imputation method that captures the simplicity of MI and protection from the DR method. This method integrates MI and DR to protect against misspecification of the imputation model under a missing at random assumption. Our method avoids analytical complications of missing data particularly in multivariate settings, and is easy to implement in standard statistical packages. Moreover, the proposed method works very well with an intermittent pattern of missingness when other DR methods can not be used. Simulation experiments show that the proposed approach achieves improved performance when one of the models is correct. The method is applied to data from the fireworks disaster study, a randomized clinical trial comparing therapies in disaster-exposed children. We conclude that the new method increases the robustness of imputations.