We employ grand canonical Monte Carlo and molecular dynamics simulations to systematically study the adsorption and diffusion of C1 to C4 alkanes in hierarchical ZSM-5 zeolite with micropores (∼1 nm) and mesopores (>2 nm). The zeolite is characterized by a large surface area of active sites on the microporous scale with high permeability and access to the active sites, which arises from the enhanced transport at the mesoporous scale. We model this zeolite as a microporous Na+-exchanged alumino-sillicate zeolite ZSM-5/35 (Si/Al = 35) in which cylindrical mesopores with a diameter of 4 nm have been built by deleting atoms accordingly. We use the TraPPE and Vujić–Lyubartsev force fields along with the Lorentz–Berthelot combining rules to describe adsorbate–adsorbate and adsorbate–adsorbent interactions. The performance of the force fields is assessed by comparing against experimental single-component adsorption isotherms of methane and ethane in microporous ZSM-5/35, which we measured as part of this work. We compare the adsorption isotherms and diffusivities of the adsorbed alkanes in the dual-porosity zeolite with those in microporous ZSM-5/35 and discern the specific behavior at each porosity scale on the overall adsorption, self-diffusion, and transport behavior in zeolites with dual micro/mesoporosities.