A theoretical method is described to simulate the propagation of turbulent premixed flames in a closed vessel. The objective is to develop and test an efficient technique to predict the propagation speed of flame as well as the geometric structure of the flame surfaces. Flame is advected by the statistically generated turbulent flow field and propagates as a wave by solving twodimensional Hamilton-Jacobi equation. In the simulation of the unburned gas flow field, following turbulence properties were satisfied: mean velocity field, turbulence intensities, spatial and temporal correlations of velocity fluctuations. It is assumed that these properties are not affected by the expansion of the burned gas region. Predictions were compared with existing experimental data for flames propagating in a closed vessel charged with hydrogen/air mixture with various turbulence intensities and Reynolds numbers. Comparisons were made in flame radius growth rate, rms flame radius fluctuations, and average perimeter and fractal dimensions of the flame boundaries. Two dimensional time dependent simulation resulted in correct trends of the measured flame data. The reasonable behavior and high efficiency proves the usefulness of this method in difficult problems of flame propagation such as in internal combustion engines.