A knowledge graph (e.g., Freebase, YAGO) is a multi-relational graph representing rich factual information among entities of various types. Entity alignment is the key step towards knowledge graph integration from multiple sources. It aims to identify entities across different knowledge graphs that refer to the same real-world entity. However, current entity alignment systems overlook the sparsity of different knowledge graphs and cannot align multi-type entities by one single model. In this paper, we present a CollectiveGraph neural network for Multi-type entity Alignment, called CG-MuAlign. Different from previous work, CG-MuAlign jointly aligns multiple types of entities, collectively leverages the neighborhood information, and generalizes to unlabeled entity types. Specifically, we propose a novel collective aggregation function tailored for this task, which (1) relieves the incompleteness of knowledge graphs via both cross-graph and self-attentions and (2) scales up efficiently with the mini-batch training paradigm and an effective neighborhood sampling strategy. We conduct experiments on real-world knowledge graphs with millions of entities and observe superior performance beyond existing methods. In addition, the running time of our approach is much less than the current state-of-the-art deep-learning methods.