We apply an interpretable Long Short-Term Memory (iLSTM) network for land-atmosphere carbon flux predictions based on time series observations of seven environmental variables. iLSTM enables interpretability of variable importance and variable-wise temporal importance to the prediction of targets by exploring internal network structures. The application results indicate that iLSTM not only improves prediction performance by capturing different dynamics of individual variables, but also reasonably interprets the different contribution of each variable to the target and its different temporal relevance to the target. This variable and temporal importance interpretation of iLSTM advances terrestrial ecosystem model development as well as our predictive understanding of the system.