In this article, we study the matrix-weighted consensus issues for second-order discrete-time multiagent systems on directed network topology. Under the designed matrix-weighted consensus algorithm, based on the eigenvalues of the Laplacian matrix, coupling gains, and discrete interval, we build some consensus conditions for reaching discrete-time consensus and deduce some simplified and straightforward consensus conditions for undirected network topology. Besides, for a given network topology, we theoretically analyze the influence of the coupling gains and discrete intervals on the consensus conditions of the network dynamics. Finally, we offer several simulation examples to validate the obtained results.