Fluid simulation requires a significant amount of computational resources because of the complexity of solving Navier-Stokes equations. In recent work [Ladický et al., 2015], a machine learning technique has been applied to only approximate, but to also accelerate, this complex and time-consuming computation. However, the prior work has not fully taken into account the fact that fluid dynamics is time-varying and involves dynamic features. In this work, we use a time-series machine learning technique, specifically the dynamic Boltzmann machine (DyBM) [Osogami et al., 2015], to approximate fluid simulations. We also propose a learning algorithm for DyBM to better learn and generate an initial part of the time-series. The experimental results suggest the efficiency and accuracy of our proposed techniques.