For achieving high-performance p-i-n perovskite solar cells (PSCs), hole transporting materials (HTMs) are critical to device functionality and represent a major bottleneck to further enhancing device stability and efficiency in the inverted devices. Three dopant-free polymeric HTMs are developed based on different linkage sites of triphenylamine and phenylenevinylene repeating units in their main backbone structures. The backbone curvatures of the polymeric HTMs affect the morphology and hole mobility of the polymers and further change the crystallinity of perovskite films. By using PTA-mPV with moderate molecular curvature, p-i-n PSCs with high efficiency of 19.5% and long-term stability can be achieved. The better performance is attributed to the more effective hole extraction ability, higher charge-carrier mobility, and lower interfacial charge recombination. Furthermore, these three polymeric HTMs are synthesized without any noble metal catalyst, and show great advantages in future application owing to the low-cost.