To investigate the influence of surface roughnesses on the dynamic characteristics of AISI 5120 steel in sliding friction process, a suite of running-in experiments are performed on a pin-on-disk tribometer. The running-in attractor is used to analyze the high-dimensional features of a friction system under different surface roughnesses. The experimental results show that the roughnesses of different original surfaces evolve to the same value in stable wear stage. The pin-on-disk friction system has a chaotic nature and exists a running-in attractor. The original surface of a disk of Ra = 0.953 μm is the most conducive to shorten the running-in duration, reduce the friction coefficient value, and improve the stability of the friction system. This roughness value is termed as the optimum surface roughness. It is an ideal working surface for the friction pair in the running-in design.