The demand of wireless spectrum is increasing very fast as the field of telecommunication is advancing rapidly. The spectrum was underutilized because of fixed spectrum assignment policy and this valuable spectrum can be utilized efficiently by cognitive radio technology. In this research we have studied spectrum selection problems in cognitive radio network. Channel sharing and channel contention problems arise when multiple secondary users tend to select same channel. The work is focused on spectrum selection issue with the aim to minimize the overall system time and to solve the problem of channel contention and channel sharing. The overall system time of secondary connection is an important performance measure to provide quality of service for secondary users in cognitive radio network.