Abstract: We propose a novel method for estimating the sparse inverse covariance matrix for longitudinal data with informative dropouts. Based on the modified Cholesky decomposition, the sparse inverse covariance matrix is modelled by the autoregressive regression model, which guarantees the positive definiteness of the covariance matrix. To account for the informative dropouts, we then propose a penalized estimating equation method using the inverse probability weighting. The informative dropout propensity parameters are estimated by the generalized method of moments. The asymptotic properties are investigated for the resulting estimators. Finally, we illustrate the effectiveness and feasibility of the proposed method through Monte Carlo simulations and a practical application.