Single-phase permeability k has intensively been investigated over the past several decades by means of experiments, theories and simulations. Although the effect of surface roughness on fluid flow and permeability in single pores and fractures as well as networks of fractures was studied previously, its influence on permeability in a random mass fractal porous medium constructed of pores of different sizes remained as an open question. In this study, we, therefore, address the effect of pore–solid interface roughness on single-phase flow in random fractal porous media. For this purpose, we apply a mass fractal model to construct porous media with a priori known mass fractal dimensions 2.579≤Dm≤2.893 characterizing both solid matrix and pore space. The pore–solid interface of the media is accordingly roughened using the Weierstrass–Mandelbrot approach and two parameters, i.e., surface fractal dimension Ds and root-mean-square (rms) roughness height. A single-relaxation-time lattice Boltzmann method is applied to simulate single-phase permeability in the corresponding porous media. Results indicate that permeability decreases sharply with increasing Ds from 1 to 1.1 regardless of Dm value, while k may slightly increase or decrease, depending on Dm, as Ds increases from 1.1 to 1.6.