Abstract: Asymmetric spatial fractional-order diffusion equations play a pivotal role in describing anomalous diffusion phenomena with bias. Examples of such phenomena include pollutant dispersion dominated by groundwater flow fields, cytoplasmic transport in complex environments, and directional edge processing in images. The present paper employs the lattice Boltzmann method to solve a class of asymmetric Riemann-Liouville spatial fractional-order diffusion equations. Firstly, the pre-processing of fractional derivatives was undertaken using linear interpolation and the mean value theorem for integrals, thereby transforming the fractional-order equation into an integer-order equation. Subsequently, employing Chapman-Enksog multiscale expansion techniques and appropriately selecting equilibrium distribution functions, a second-order accurate lattice Boltzmann model was established. The final stage of the research process involves the validation of the proposed model's validity through numerical experiments. The results obtained demonstrate that the numerical outcomes of the model exhibit good agreement with the exact solutions under various weighting functions and fractional orders.