Two novel fast consensus algorithms based on local information of first-order discrete multi-agent systems under a directed network are proposed in this paper. By applying matrix theory and the frequency-domain analysis methods, two sufficient conditions about the convergence rate of the systems are presented, respectively, where the proportional-like gain feedback and incremental proportional-integral-differential gains feedback only with local information are added. Finally, a numerical example is given to show the double gains regulation algorithm proposed in this paper has much faster consensus rate compared with the classical consensus algorithm in the same condition for its two-degree freedom parameters.