In Cognitive Radio(CR) networks,CR user has to detect the spectrum channel periodically to make sure that the channel is idle during data transmission frame in order to avoid the collisions to the primary users.Hence recent research has been focused on the interference avoidance problem.Quality of Service(QoS) requirement of CR user will affect the time of data transmission in each frame.In this paper,in order to solve the interference avoidance and spectrum utilization problems without cooperation among CR users,a new scheme to obtain the optimal duration of data transmission frame is proposed to maximize the spectrum utilization and guarantee the protection to the primary users.The main advantages of our proposed scheme include the followings:(1) QoS requirement of CR user is concerned;(2) p-persistent Media Access Control(MAC) random access is used to avoid the collisions among CR users;(3) CR network system capacity is considered.We develop a Markov chain of the primary spectrum channel states and an exponential distribution of the CR user’s traffic model to analyze the performance of our proposed scheme.Computer simulation shows that there is an optimal data transmission time to maximize the spectrum utilization.However,the regulatory constraint of the collision rate to the primary users has to be satisfied at the expense of spectrum utilization.And also the tradeoff between the spectrum utilization and the capacity of the CR system is taken into account. In Cognitive Radio (CR) networks, CR user has to detect the spectrum channel period to make sure that the channel is idle during data transmission frame in order to avoid the collisions to the primary users .Hence recent research has been focused on the interference avoidance problem. Quality of Service (QoS) requirement of CR user will affect the time of data transmission in each frame. In this paper, in order to solve the interference avoidance and spectrum utilization problems without cooperation among CR users, a new scheme to obtain the optimal duration of data transmission frame is proposed to maximize the spectrum utilization and guarantee the protection to primary user.The main advantages of our proposed scheme include the followings: (1) QoS requirement of CR user is concerned; (2) p-persistent Media Access Control (MAC) random access is used to avoid collisions among CR users; (3) CR network system capacity is considered. We develop a Markov chain of the primary spectrum ch annel states and an exponential distribution of the CR user’s traffic model to analyze the performance of our proposed scheme. Computer simulation shows that there is an optimal data transmission time to maximize the spectrum utilization. However, the regulatory constraint of the collision rate to the primary users has to be satisfied at the expense of spectrum utilization. And also the tradeoff between the spectrum utilization and the capacity of the CR system is taken into account.