For the rendezvous problem of the Lagrange vehicles with quantized data exchange and communication delay, a model-dependent and discontinuous right-hand side control algorithm was proposed, and a uniform quantizer was designed. The stability of controller was considered by using the graph, matrix theory, and the practical stability theory. It was shown that the rendezvous with error bound is rigorously proven in an undirected topology via quantized data exchange and communication delay. The numerical example based on MATLAB software also verifies the effectiveness of the algorithms.