The roughness of pores has an important effect on fluid flow in porous media. In order to study this effect, it is necessary to generate porous media models with precisely controlled morphology. In recent years, researchers have used correlated random fields theory to generate porous media models. However, they have paid little attention to the effect of roughness. Unlike previous methods using Gaussian covariance function, the Matérn covariance function is utilized. Through this function, the roughness of the porous media models can be precisely controlled. A number of 3D porous media models with similar pores distribution, gradually changing roughness are generated. Then, using 3D printing technology, some specimens are produced based on geometric models. Afterwards, a specimen is characterized using micro-CT, to verify the quality of the printing. Finally, the effective porosity ratio, tortuosity, specific surface area and fractal dimension of pore surfaces of the geometric models and 3D printed samples are analyzed.