In this paper, we investigate a networked control problem in the presence of Denial-of-Service (DoS) attacks, which prevent transmissions over the communication network. The communication between the process and controller is also subject to bit rate constraints. For mitigating the influences of DoS attacks and bit rate constraints, we develop a variable bit rate (VBR) encoding-decoding protocol and quantized controller to stabilize the control system. We show that the system's resilience against DoS under VBR is preserved comparing with those under constant bit rate (CBR) quantized control, with fewer bits transmitted especially when the attack levels are low. The proposed VBR quantized control framework in this paper is general enough such that the results of CBR quantized control under DoS and moreover the results of minimum bit rate in the absence of DoS can be recovered.