**Abstract:**
Fish population dynamics demonstrates the quantitative changes in the number of individuals in which a given fish population grows and shrinks over time as controlled by some specific factors, and is generally used in the fisheries science in order to determine sustainable yields. The aim of this article is to present and analyze a generic mathematical formula of a single-region size structured model which is useful for the fish production estimation. With the intention to estimate the final fish size, the von Bertalanffy’s growth equation is modified and utilized based on the initial size of the fish species. For fish population calculation, initial size, birth, growth, mortality rates and the arbitrary constant of modified von Bertalanffy’s growth equation are considered as input variables. The number of total fish population and the fish size at different time spans are calculated. The results coming from the mathematical calculation are compared to the experimental results of freshwater mud eel fish production. Comparing to these values, it reveals that there is no significant difference between the result obtained by implementing the proposed mathematical model and the experimental outcomes obtained. Finally, it is expected that the modified model can be used for the practical applications of fish production.

**Keywords:**
Mathematical estimation; Fish population; Fish size; Mortality rates; von Bertalanffy’s growth equation.