One of the main goals stated in the proposals for the Common Fisheries Policy (CFP) reform was achieving maximum sustainable yield (MSY) for all European fisheries. In this paper, we propose a fishing rights allocation mechanism or management system, which specifies catch limits for individual fishing fleets to implement MSY harvesting conditions in an age-structured bioeconomic model. An age-structured model in a single species fishery with two fleets having perfect or imperfect fishing selectivity is studied. If fishing technology or gear selectivity depends on the relative age composition of the mature fish stock, fixed harvest proportions, derived from catchability and bycatch coefficients, is not valid anymore. As a result, not only the age-structure and fishing technology but also the estimated level of MSY is steering the allocation of quota shares. The results also show that allocation of quota shares based on historical catches or auctioning may not provide viable solutions to achieve MSY. (C) 2016 Elsevier Inc. All rights reserved.