Anchor Link Prediction (ALP) across heterogeneous networks plays a pivotal role in inter-network applications. The difficulty of anchor link prediction in heterogeneous networks lies in how to consider the factors affecting nodes alignment comprehensively. In recent years, predicting anchor links based on network embedding has become the main trend. For heterogeneous networks, previous anchor link prediction methods first integrate various types of nodes associated with a user node to obtain a fusion embedding vector from global perspective, and then predict anchor links based on the similarity between fusion vectors corresponding with different user nodes. However, the fusion vector ignores effects of the local type information on user nodes alignment. To address the challenge, we propose a novel type-aware anchor link prediction across heterogeneous networks (TALP), which models the effect of type information and fusion information on user nodes alignment from local and global perspective simultaneously. TALP can solve the network embedding and type-aware alignment under a unified optimization framework based on a two-layer graph attention architecture. Through extensive experiments on real heterogeneous network datasets, we demonstrate that TALP significantly outperforms the state-of-the-art methods.