Recently, some papers that apply a multi-armed bandit algorithm for channel selection in a cognitive radio system have been reported. In those papers, channel selection based on Upper Confidence Bound (UCB) algorithm has been proposed. However, in those selection, secondary users are not allowed to transmit data over same channels at the same time. Moreover, they do not take security of wireless communication into account. In this paper, we propose secure channel selection methods based on UCB algorithm, taking secrecy capacity into account. In our model, secondary users can share same channel by using transmit time control or transmit power control. Our proposed methods lead to be secure against an eavesdropper compared to conventional channel selections based on only estimated channel availability. By computer simulation, we evaluate average system secrecy capacity. As a result, we show that our proposed channel selections improve average system secrecy capacity compared to conventional channel selection.