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Electrostatic superlattices have been known to significantly modify the electronic structure of low-dimensional materials. Studies of graphene superlattices were triggered by the discovery of moiré patterns in van der Waals stacks of graphene and hexagonal boron nitride (hBN) layers a few years ago. Very recently, gate-controllable superlattices using spatially modulated gate oxides have been achieved, allowing for Dirac band structure engineering of graphene. Despite these rapid experimental progresses, technical advances in quantum transport simulations for large-scale graphene superlattices have been relatively limited. Here, we show that transport experiments for both graphene/hBN moiré superlattices and gate-controllable superlattices can be well reproduced by transport simulations based on a scalable tight-binding model. Our finding paves the way to tuning-parameter-free quantum transport simulations for graphene superlattices, providing reliable guides for understanding and predicting novel electric properties of complex graphene superlattice devices. The electronic structure of graphene can be modified by applying the so-called superlattice potential, arising either from interfacing with hexagonal boron nitride lattices or gate capacitance with spatially periodic modulation, giving rise to a range of unusual transport behavior. Here, the authors report a simulation method to reproduce transport experiments, showing consistent transmission spectra and mini-band structures for graphene superlattices. [ABSTRACT FROM AUTHOR]