Databases are used in many applications, spanning virtually the entire range of data processing services industry. The data in many database applications can be most naturally represented in the form of a graph structure consisting of various types of nodes and edges with several properties. These graph data can be classified into four categories: social networks describing the relationships between individual person and/or groups of people (e.g. genealogy, network of coauthorship among academics, etc); information networks in which the structure of the network reflects the structure of the information stored in the nodes (e.g. citation network among academic papers, etc); geographic networks, providing geographic information about public transport systems, airline routes, etc; and biological networks (e.g. biochemical networks, neuron network, etc). In order to analyze such networks and obtain desired information that users are interested in, some typical queries must be conducted. It can be seen that many of the query patterns are across multiple categories described above, such as finding nodes with certain properties in a path or graph, finding the distance between nodes, finding sub-graphs, paths enumeration, etc. However, the classical query languages like SQL, OQL are inept dealing with these types of queries needed to be performed in the above applications. Therefore, a data model that can effectively represent the graph objects and their properties, and a query language which empowers users to answer queries across multiple categories are needed. In this research work, a graph data model and a query language are proposed to resolve the issues existing in the current database applications. The proposed graph data model is an object-oriented graph data model which aims to represent the graph objects and their properties for various applications. The graph query language empowers users to query graph objects and their properties in a graph with specified conditions. The capability to specify the relationships among the entities composing the queried sub-graph makes the language more flexible than others.