A transition model applied to a new low Reynolds number two equation turbulence model that characterizes the near-wall turbulence behavior is proposed to improve the transition prediction for the flat plate flow. The newly developed two-equation model utilizes the largest and the smallest scales in constructing the turbulent eddy viscosity model, including the damping effects to match the asymptotic behavior of the flow in the vicinity of the wall. Two types of damping functions were presented and tested against the simple flows from DNS data. Transition predictions using this two-equation model at bypass free stream turbulence levels were not agreed well with experimental correlation. Focus on the production term in the turbulent kinetic energy transport equation was carried out and a convective production transition model was then proposed, Numerical results compared with the onset and end of transition experimental data were found to be appropriate.