To improve the coupling efficiency of a conventional Ti:LiNbO3 channel waveguide with a single mode fibre, a promising Ti-Mg double diffused method has been employed to fabricate a single mode power divider. Calculated numerical results have revealed the feasibility of reducing coupling loss as well as radiation loss, and a set of efficient fabrication parameters for this single mode device can be established. The dependence of asymmetric branching angles and output dividing-power-ratios has been studied by adjusting the branching angle.