Stochastic analysis is applied to a Cauchy problem for a scalar conservation lawby using “vanishing viscosity” method . It is proved that the stochastic characteristic of equationconverges to the characteristic of equation. In this way a well known result is recovered, that is, the solution ofconverges to the entropy solution ofnaturally. Entropy condition is crucial to the proofs. The result suggests that the new method, stochastic analysis, may be useful for solving difficult problems of quasi-linear partial differential