Social-aware recommendation approaches have been recognized as an effective way to solve the data sparsity issue of traditional recommender systems. The assumption behind is that the knowledge in social user-user connections can be shared and transferred to the domain of user-item interactions, whereby to help learn user preferences. However, most existing approaches merely adopt the first-order connections among users during transfer learning, ignoring those connections in higher orders. We argue that better recommendation performance can also benefit from high-order social relations. In this paper, we propose a novel Propagation-aware Transfer Learning Network (PTLN) based on the propagation of social relations. We aim to better mine the sharing knowledge hidden in social networks and thus further improve recommendation performance. Specifically, we explore social influence in two aspects: (a) higher-order friends have been taken into consideration by order bias; (b) different friends in the same order will have distinct importance for recommendation by an attention mechanism. Besides, we design a novel regularization to bridge the gap between social relations and user-item interactions. We conduct extensive experiments on two real-world datasets and beat other counterparts in terms of ranking accuracy, especially for the cold-start users with few historical interactions.