This paper presents a method for estimating a class of panel data duration models, under which an unknown transformation of the duration variable is linearly related to the observed explanatory variables and the unobserved heterogeneity (or frailty) with completely known error distributions. This class of duration models includes a panel data proportional hazards model with fixed effects. The proposed estimator is shown to be n1/2-consistent and asymptotically normal with dependent right censoring. The paper provides some discussions on extending the estimator to the cases of longer panels, multiple states, and endogenous explanatory variables. Some Monte Carlo studies are carried out to illustrate the finite-sample performance of the new estimator.