This paper proposes an estimation procedure for the semiparametric accelerated failure time frailty model that combines smoothing with an Expectation and Maximization-like algorithm for estimating equations. The resulting algorithm permits simultaneous estimation of the regression parameter, the baseline cumulative hazard, and the parameter indexing a general frailty distribution. We develop novel moment-based estimators for the frailty parameter, including a generalized method of moments estimator. Standard error estimates for all parameters are easily obtained using a randomly weighted bootstrap procedure. For the commonly used gamma frailty distribution, the proposed algorithm is very easy to implement using widely available numerical methods. Simulation results demonstrate that the algorithm performs very well in this setting. We re-analyz several previously analyzed data sets for illustrative purposes. Copyright © 2012 John Wiley & Sons, Ltd.