In this paper, we study the secrecy capacity of an underlay cooperative cognitive radio network (CCRN) where multiple relays are deployed to assist the secondary transmission. An optimal power allocation algorithm is proposed for the secondary transmitter and secondary relays to obtain the maximum secrecy capacity while satisfy the interference power constraint at the primary receiver and the transmit power budget of the CCRN. Since the optimization problem for the secrecy capacity is non-convex, we utilize an approximation and fitting method to convert the optimization problem into a geometric programming problem which then is solved by applying the Logarithmic barrier function. Numerical results are provided to study the effect of network parameters on the secrecy capacity. Through the numerical results, the advantage of the proposed power allocation algorithm compared to equal power allocation can also be observed.