Aimed at the characteristics of cognitive Ad hoc network, a corresponding network model is established and a distributed power control algorithm based on convex optimization theory is proposed. Based on the analysis of system interference, by taking the network utility maximization as the target and transmit power of cognitive user as the solution object, a general math optimized model is formulated. Under the guidance of convex optimization theory, the model is transformed into a convex optimized model by introducing auxiliary variable and substituting variables. Lagrangian dual decomposition technique is used to solve the convex optimized model and the distributed power iterative algorithm is obtained. The simulation shows that under the premise of meeting the system constraints, the use of the proposed algorithm can obtain better system performances than that of other algorithms.