As the existing distributed subgradient optimization algorithms are mainly based on ideal assumptions:the network topology is balanced and the communication among the network is usually the exact information of a state variable of each agent. To relax these assumptions, a distributed subgradient optimization algorithm for switched networks was proposed based on limited quantized information communication. All information along each dynamical edge was quantified by a uniform quantizer with a limited quantization level before being sent in an unbalanced switching network, then the convergence of the multi-agent distributed quantized subgradient optimization algorithm was proved by using non-quadratic Lyapunov function method. Finally, the simulation examples were given to demonstrate the effectiveness of the proposed algorithm. The simulation results show that, under the condition of the same bandwidth, the convergence rate of the proposed optimization algorithm can be improved by adjusting the parameters of the quantizer. Therefore, the proposed optimization algorithm is more suitable for practical applications by weakening the assumptions on the adjacency matrix and the requirement of the network bandwidth.