The consensus problem for double-integrator dynamics under fixed and directed interaction in a discrete-time setting is studied. A distributed control protocol based on velocity and position is designed for each agent, and the impact of velocity and position gains and sampling period on consensus is analyzed. Results show that consensus of the second-order multi-agent system can be achieved if and only if the topology graph has a directed spanning tree and the values of the gain parameters meet some constraints. Both eigenvalues of the corresponding Laplacian matrix and sampling period play a key role in reaching asymptotical consensus. A general parameter design method for consensus problem is proposed. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of the theoretical results.