Propagation characteristics of tribrachial flames have been studied numerically in a two-dimensional fuel/oxidizer mixing layer. A flame is initiated by imposing a high temperature ignition source. Subsequent propagation of a tribrachial flame is traced. The flow redirection effect at the leading edge of a tribrachial flame increases the propagation speed beyond the corresponding stoichiometric laminar burning velocity. The effect of mixture fraction gradient on the propagation speed of a tribrachial flame is analyzed in a mixing layer considering that mixture fraction gradient increases as a tribrachial flame propagates toward upstream. As the flame curvature at the leading edge increases with decreasing mixture fraction gradient, the flow redirection effect becomes more pronounced on the flame propagation speed. As a result, the propagation speed of a tribrachial flame increases with decreasing mixture fraction gradient.