A novel semi-Lagrangian computational method has been developed in order to determine an accurate solution to the fluid mixing problem with a given velocity field in a T-shaped micromixer. Its trajectory-based fractional discretization scheme consists of a grid-based expression of a Laplacian with a spatial interpolation and a Lagrangian expression of convective transport by backward tracer particle tracking. The present numerical simulations provide high accuracy with negligible numerical diffusion for any grid orientations. The solutions to convective mixing in an engulfment flow regime of a T-shaped micromixer at Re = 200 for various values of Sc from 1 to 1000 are compared with those obtained from a conventional grid-based method and a backward random-walk Monte Carlo method. The results of the proposed method are shown to agree well with those of the Monte Carlo method for all conditions, while the grid method presents large discrepancies due to unavoidable numerical diffusion at large values of Sc even with 16 million cells. It is demonstrated that the present method requires considerably lesser CPU time to achieve an accuracy equal to that obtained with the Monte Carlo method.