Networked control systems (NCSs) have been receiving much attention in order to improve control performance in the field of in remote robot operation, surgery and some operations. In the NCSs, it is important to quantize necessary signals for control over a limited network channel for the sake of prevention from transmitting a large amount of data. This paper addresses a quantized feedback control system with a variable discrete quantizer. In the system, both input and a parameter of the quantizer are optimized online with the help of model predictive control (MPC). In our approach, constraints on input/output, the parameter of the quantizer and other physical and/or logical constraints can be explicitly taken into account while guaranteeing optimality. The optimization problem is reduced to a mixed integer quadratic programming. Experimental results are demonstrated to verify the effectiveness of the proposed method.