This study aimed at determining the market structure of Real Estate Investment Trusts in Nigeria (N-REITs) with a view to providing information for investment decisions. The population relevant for this study consisted of all the N-REITs companies in Nigeria namely Skye Shelter Fund, Union Homes REITs and UPDC REITs. A total enumeration survey of all the three companies was carried out. Relevant data from 2008 to 2016 on the market share and concentration ratio in the N-REITs industry which were subsequently translated to the Herfindahl Hischman Index (HHI) were obtained from the respective companies. The data were analyzed by means of descriptive statistical tools. Findings from the study revealed an HHI that ranged between 4181 and 10000. This showed a high concentration in the N-REITs industry indicating an oligopolistic market structure. This study implies that there is need for the Nigerian Security Exchange Commission (SEC) to take measures that can encourage more establishment of REITs companies to facilitate more competition in the industry and move it towards being a perfect competitive market structure like the US, UK and Japan. One of the characteristics of oligopolistic markets is the absence of competition which generally makes the companies rest on their oars. Creation of more REITs companies (through provision of enabling environment in the REITs sector) will liberalize the market and make it more competitive which will invariably improve the return performance of the industry.