The Sampling Kaczmarz-Motzkin (SKM) algorithm is a generalized method for solving large-scale linear system of inequalities. Having its root in the relaxation method of Agmon, Motzkin and the randomized Kaczmarz method, SKM outperforms the state-of-the-art methods in solving large-scale linear feasibility problems. Motivated by SKM’s success, in this work, we propose an Accelerated Sampling Kaczmarz-Motzkin (ASKM) algorithm which achieves better convergence compared to the standard SKM algorithm on ill conditioned problems. We provide a thorough convergence analysis for the proposed accelerated algorithm. We validate the convergence analysis with a set of numerical experiments on randomly generated linear system of inequalities.