This paper addresses the quantized consensus problem of continuous-time second-order multi-agent systems via sampled data where the interconnection topology has a directed spanning tree. A necessary and sufficient condition on the sampling period and the design parameters is obtained to guarantee that the consensus errors converge to a neighborhood of the origin which disappears as the quantized errors tend to zero. This paper also gives the final consensus values, which is different from the existing works on the quantized consensus of second-order multi-agent systems. The method is further extended to the case when the velocities of agents are unavailable. Two simulation examples are provided to illustrate the effectiveness of the proposed consensus protocols. (C) 2013 Elsevier Ltd. All rights reserved.