In recent decades, the river network patterns (RNPs) in China’s Haihe River basin have changed dramatically, and the topology of the river network has become increasingly complex. It is important to quantitatively study the correlation between river network patterns and topography (CRNPT) and the changes in the correlation. In this paper, the Haihe River basin was spatially gridded (4 km × 4 km), and different geomorphological areas were extracted for a multiarea study. We selected topographic and river network indicators and proposed new indicators to characterize regional topographic ‘stressfulness’ and then used redundancy analysis for correlation studies. The results showed that the variance of RNP explained by topography was 53.39%. The combined contribution of the topographic wetness index (TWI) and topographic wetness stress index (TSI) ranged from 35.66% to 78.29% in multiple areas, and the TSI showed stronger explanatory power. The regional effect of the CRNPT was significant, with mountains and transition areas having higher effects than plain areas. Compared to the natural river network, the CRNPT of the current river network was significantly lower. Among the RNP indicators, the artificial channel proportion (Pac) had the highest proportion of variance, and the CRNPT was strongly influenced by artificial channels. Artificial channels changed the consistency of topography with the RNP and reduced the topographic interpretation of the RNP, which may weaken the stability and hydrological connectivity of the river network. The variation in interpretation was related to the distribution of artificial channels, which showed a logarithmic function relationship between them.