To improve the photovoltaic performance of fullerene-free organic solar cells (OSCs), the domain size of the polymer blend film is often reduced using low-volatility solvents and additives. However, since the resulting film is thermodynamically unstable, chemical modification of the polymer is necessary to obtain small domain size from low crystallinity. In this study, we synthesized a new random π-conjugated polymer (asy-PBDTPBT) and investigated the effect of its structural irregularity arising from random copolymerization and from introducing an asymmetric third component. The crystallinity of asy-PBDTPBT was remarkably lower than that of the control polymer (PBDTP) owing to its higher degree of irregularity. According to the tendency of this irregularity, non-fullerene OSCs using asy-PBDTPBT (power conversion efficiency (PCE) of 8.22%) outperformed those using PBDTP (7.37%).