The propagation of vector solitons in nonlocal nonlinear media with a Gauss barrier or a Gauss trap is described by the coupled nonlocal nonlinear Schrodinger equations with Gauss-type linear potential. These equations are numerically calculated by the square operator method, and the propagation of vector solitons is simulated by the step-step method. In nonlocal nonlinear bulk media, the components of out-of-phase vector solitons are always separated spontaneously, and the repulsion between them can be suppressed by a Gauss barrier. The components of in-phase vector solitons are always fused spontaneously, and the attraction between them can be suppressed by a Gauss trap. By quantitatively analyzing the relationship between the barrier heigh/depth or width and the distance between two components of vector solitons at the normalized transmission distance of 500, it is found that if the heigh/depth and width of barrier/trap are too large or too small, Gauss linear potential can not suppress this process, or even worsen it. For out-of-phase solitons, the Gauss barrier that can effectively suppress the separation should be set to 1.10 in height and 1.00 in width. For in-phase solitons, the Gauss potential well that can effectively suppress the fusion should be set to －1.50 in depth and 1.00 in width. Results in this paper may benefit the future researches about all-optical switch, optical logic-gate, optical computing and other optical control technologies.