This paper investigates the sampled-data based consensus problem of first-order multi-agent systems with quantized communication. A deterministic consensus protocol with the logarithmic quantizer proposed in the literature is reinvestigated. A new sufficient condition is derived under which consensus is achieved. It is proved that for any network topology that has a directed spanning tree, consensus is achieved if the quantization accuracy parameter and the sampling period are small enough. A numerical example is given to illustrate the theoretical results.