With the widespread deployment of various cloud computing and service-oriented systems, there is a rapidly increasing demand for collaborative quality-of-service (QoS) prediction. Existing QoS prediction methods have made great progress in modeling users and services as well as exploiting contexts of service invocations. However, they ignore the completion of service requests/responses relies on the underlying network topology and the complex interactions between Autonomous Systems. To tackle this challenge, we propose a topology-aware neural (TAN) model for collaborative QoS prediction. In the TAN model, the features of users, services, and intermediate nodes on the communication path are projected to a shared latent space as input features. To jointly characterize the invocation process, the path features and end-cross features are captured respectively through an explicit path modeling layer and an implicit cross-modeling layer. After that, a gating layer fuses and transmits these features to the prediction layer for estimating unknown QoS values. In this way, TAN provides a flexible framework that can comprehensively capture the invocation context for making accurate QoS prediction. Experimental results on two real-world datasets demonstrate that TAN significantly outperforms state-of-the-art methods on the tasks of response time, throughput, and reliability prediction. Also, TAN shows better extensibility of using auxiliary information.