This paper develops a new technique for estimating mixed logit models with a simple minorization–maximization (MM) algorithm. The algorithm requires minimal coding and is easy to implement for a variety of mixed logit models. Most importantly, the algorithm has a very low cost per iteration relative to current methods, producing substantial computational savings. In addition, the method is asymptotically consistent, efficient and globally convergent. Copyright © 2016 John Wiley & Sons, Ltd.