This paper investigates the problem of the global directed dynamic behaviors of a Lotka-Volterra competition-diffusion-advection system between two species in heterogeneous environments, where two species are competing for different fundamental resources, their advection and diffusion strategies follow a positive diffusion distribution, the functions of inter-specific competition ability are variable. By virtue of the principal eigenvalue theory, the linear stability of the co-existing steady state is established. Furthermore, the classification on all possible long-time dynamical behaviors is shown by utilizing the monotone dynamical system theory.