In this paper we study secure communications with weak secrecy constraint in a cognitive radio channel, where the secondary receiver is treated as a potential eavesdropper with respect to the primary transmission. The primary's secrecy rate and the transmission scheme should be kept unchanged whether the secondary users transmit or not. We derive the achievable rate of the discrete memoryless multi-phase cognitive channel. To against the information leakage due to the use of Gelfand-Pinsker coding at the secondary transmitter, we derive the corresponding constraints to guarantee the primary's secure transmission. We then specialize the results to the additive white Gaussian noise channels. Numerical results show the advantages of using the proposed multiple-phase transmission scheme over the traditional ones without the additional phase.