The laminar flame propagation in narrow confined disc-shape chambers of millimeter scale is investigated, concerning the flame front displacement speed and the influences from the changes of the gap width and radius. An asymptotic analysis treating the flame front as a discontinuity successfully predicts the velocity profiles of the flame front and illustrates the importance of heat release parameter and laminar flame speed of the fuel. The unsteady flame propagation process is simulated by a full numerical computation which employs the n-butane/air mixture as the reactant. The numerical simulation emphasizes the sensitivity of spatial scale to the flame propagation in narrow spaces, indicating that the acceleration rate and the maximum speed of the flame have a non-monotonic relation with the gap width, of which the optimal value is about 0.8 mm. Faster flame propagation is favored for larger gap radius due to stronger flame straining, but it is restricted by the gap width.