One of the most important issues in the world literature is to measure and assess the degree of competitiveness and monopoly in the markets and determine the structure of the international market. One of the main goals of countries in the world of trade has long been gaining a greater share of the international market. Iran is one of the largest pomegranate producers and exporters in the world. The present study evaluates Iran's pomegranate demand by using parametric models and panel data for countries exporting pomegranates from Iran during the period of 1993 to 2013. The results showed that the price elasticity of the pomegranate demand is -0.06. This means that as prices rise, there is no significant reduction in the demand of the importing countries, and it shows demand of Iran pomegranate in the global market is inelastic. These results are consistent with the calculation indices of the Herfindahl – Hirschman, share of two largest firms and eight largest firms in the pomegranate world market structure, which highlights the strong focus of the market for Iran and India. It seems that that the continuation of the current process may endanger Iran's market power and position. Finding new business models, marketing and participating in international exhibitions are some of the strategies to maintain and expand Iran's pomegranate demand in global markets.