A novel backward Euler integration-based generalized discrete reaching law is proposed for the numerical chattering in the traditional forward Euler approximation of reaching law. Firstly, the proposed reaching law exhibits globally chattering-free convergence, and releases more freedom degrees for parameter design. Moreover, the influence relationship of parameters on the convergence rate of sliding variables is established, which provides a theoretical foundation for parameter tuning. Finally, when taking into account the uncertainty of systems, the final boundary layer of sliding surface is deduced, and it is proved that the designed reaching law can guarantee the fast transient response and high-precision control of the closed-loop system at the same time. Numerical simulations validate the effectiveness of the proposed algorithm.