In this paper, we focus on solving the system of absolute value equations (AVE), which is one of the most popular classes of nonlinear equations. First, a new smoothing technique with three different smoothing functions is introduced, and the AVE is transformed into a family of parametrized smooth equations with the help of these smoothing functions. Then, a smoothing Newton-type algorithm with hybridized inexact line search is developed based on the proposed smoothing technique. The numerical experiments have been carried out on some well-known and randomly generated test problems, and the results are analyzed in terms of line search techniques. The numerical results show that the proposed hybrid approach is more efficient than the other algorithms.