The recent development of maritime transport has resulted in the demand for a wider communication bandwidth being more intense. Cognitive radios can dynamically manage resources in a spectrum. Thus, building a new type of maritime cognitive radio communication system (MCRCS) is an effective solution. In this paper, the enhanced dynamic spectrum allocation algorithm (EDSAA) is proposed, which is based on the Cournot game model. In EDSAA, the decision-making center (DC) sets the weights according to the detection capability of the secondary user (SU), before adding these weighting coefficients in the price function. Furthermore, the willingness of the SU will reduce after meeting their basic communication needs when it continues to increase the leasable spectrum by adding the elastic model in the SU’s revenue function. On this basis, the profit function is established. The simulation results show that the EDSAA has Nash equilibrium and conforms to the actual situation. It shows that the results of spectrum allocation are fair, efficient and reasonable.