Facing the large amount of name mentions appearing on the web, entity linking turns to be a hot researching topic recently, in which an entity in a resource is assigned to one name mention to help users grasp the meaning of this name mention. Unfortunately, like word disambiguation, one name mention can refer to several entities without considering its context. Apparently, the name mentions that ... [Show full abstract] usually co-occur are related and can be considered together to determine their suitable entities. This approach is called collective entity linking and is often conducted based on entity graph. However, traditional collective entity linking methods either consume much time due to the large scale of entity graph or obtain low accuracy due to simplifying graph to boost speed. To improve both accuracy and efficiency, this paper proposes a novel collective entity linking algorithm. It constructs a complete entity graph by connecting any two related entities, and the relationship between two entities is measured via a random walk-based calculating way. After that the relationships between entities are modeled as a relationship matrix, and a hill-climbing-based algorithm is proposed to change entity linking task to a sub-matrix searching problem. Experimental results demonstrate that our linking algorithm can obtain both accurate linking results and low running time meanwhile.