Shock wave in a random system has been investigated theoretically and experimentally. A nonlinear LC ladder circuit with random inhomogeneity of linear inductor in series branch has been studied. The circuit is equivalent to a random Toda lattice. It is shown theoretically that wave propagation in the system is described by the Burgers equation in the case of strong randomness with weak nonlinearity. The transition from an oscillatory shock wave to a shock wave has been observed on a random LC ladder circuit experimentally. The velocity and width of shock wave agree with the theoretical prediction from the Burgers equation in a region of strong randomness.