Tracer transport is a critical computational bottleneck in high-resolution atmospheric chemistry models, where tens to hundreds of species are advected. The iAMAS model (v2.6.3) on spherical centroidal Voronoi tessellations (SCVTs) currently employs a scheme (2H1FCT) that performs two steps of third-order transport followed by one step of flux-corrected transport (FCT), in which the FCT correction step dominates computational cost. This study develops TVD-FFSL, a computationally efficient hybrid tracer transport scheme. Horizontally, a total variation diminishing (TVD) flux operator with the KOREN limiter is employed. Vertically, a flux-form semi-Lagrangian (FFSL) operator based on piecewise parabolic method reconstruction handles cells with CFL > 1unconditionally. Together with a second-order TVD Runge-Kutta time integration, the scheme ensures monotonicity without a separate FCT step. Idealized 2D tests demonstrate that TVD-FFSL achieves robust shape preservation. Although its errors are slightly higher than 2H1FCT, superior convergence rates render the accuracy gap negligible at finer resolutions (∆<em>x</em> ≤ 30 km). Realistic 3D dust simulations on a 16–60 km variable-resolution grid confirm its long-term stability and accuracy comparable to 2H1FCT. Performance benchmarks show that TVD-FFSL achieves over 2× speedup in standalone transport tests and exceeds 3.75× speedup in long-term atmospheric dust simulations, significantly reducing the computational overhead of numerous tracer transport. The design principles of TVD-FFSL could be transferable to other unstructured meshes, offering a pathway toward accelerating high-resolution atmospheric chemistry simulations.