The aim of this chapter is to design matrix-weighted consensus algorithms with a faster convergence rate. These algorithms are divided into two types: memoryless and memory-based accelerated algorithms. In memoryless algorithms, the control efforts are concentrated to stabilize the system in a finite time. The side effect is a high control magnitude at the beginning of the system’s trajectory. Given the same initial condition, the faster the algorithm is, the higher the peak of the control magnitude will be expected. The second type of accelerated algorithms uses both present and past information to enhance the convergence speed. The past values are padded into a queue of fast registers for being added to the current control input. As the trade-offs for a better convergence speed of the consensus network, more memories and computing power are required for each agent. Furthermore, the convergence speed can only be enhanced in a limited range, and the updating gains allocated for the present and outdated information should be carefully chosen to improve the convergence speed.