An age-structured bioeconomic model, which is completely continuous in age and time, is developed in order to compare with traditional discrete models. Both types have advantages and disadvantages. The continuous framework complements discrete models as it allows for deeper and more transparent analytical study and leads to analytical results that would be difficult to achieve within a discrete framework. To make the model realistic, a nonlinear recruitment function is introduced and steady state solutions and constant-effort optimal fishing are studied analytically. In addition, the framework has been used for numerical analysis. Simulations are used to investigate how optimal harvesting patterns vary with parameter values.