Relational databases have been prevailing for the last two decades, with features of clear semantics and ease of use with SQL supported by the underlying theory, relational algebra. Relational databases provide good support for structural data management. However, recent development in IT brings forward big data, featuring extreme large volume and variety in data type and structures, and relational databases are difficult to handle such big data due to the strict constraints on data structure and data relations, and so on. On the other hand, NoSQL databases, including HBase, MongoDB, Cassandra, etc., are receiving their popularity for their capability in dealing with large amount of complex data in various structures. Currently there is no way to know the feasibility of the migration of traditional relational databases to NoSQL databases. The migration requires evaluating the feasibility of the migration and potential performance of the new systems. This paper investigates these issues by modelling one of the NoSQL database, MongoDB, with relational algebra. The modelling will allow the comparison of semantic expression powers between relational databases and MongoDB, analysing the feasibility of the migration of a relational database to MongoDB and its evaluation. The model is expected to facilitate the optimization of the new NoSQL database.