This paper investigates the problem of rendezvous with connectivity preservation for a group of mobile agents subject to both unknown input delay and unknown communication delay. We propose a new potential function and design a potential function based distributed control law. To tackle unknown time delays, we introduce a control gain in the control law and develop an energy functional to characterize the energy of the whole system. By analyzing the energy change, the control gain is designed. It is shown that as long as the communication network is connected at the initial time, the proposed control law can make all agents reach the same location and maintain connectivity of the communication network for all time. Meanwhile, it can accommodate arbitrarily bounded uniform constant input delay and communication delay. (C) 2017 Elsevier Ltd. All rights reserved.