The main purpose of this study is to investigate the local velocity acceleration in a boundary layer diffusion flame over a flat plate. In order to know the effect of separation on the local velocity acceleration, two typical cases, flows with and without separation, are considered. For these cases, flow visualization using paraffine smoke tracers has been made. Mean velocity and r.m.s. value of fluctuating velocity are measured by using a laser Doppler velocimeter. In addition, measurements of time-mean concentration and time-mean temperature have been made. Time-mean density profiles have been obtained from the data of concentration and temperature. The obtained results are summarized as follows : (1) In the case without separation, the local velocity acceleration is clearly observed near the visible flame zone for all flow conditions. On the while, in the case with serration, the local velocity acceleration is observed only at low free stream velocity and high fuel injection velocity. As increasing the free stream velocity or decreasing the fuel injection velocity, it is not distinctly observed in the mean velocity profile. (2) The r.m.s. value of fluctuating velocity is significantly decreased by combustion in the case with separation. But in the case without separation, the r.m.s. value is increased near the visible flame zone in comparison with cold flow. In both cases, the peak value of r.m.s. appeared just at the visible flame zone, where the mean velocity gradient is not too high.