To decrease the numerical error in the engineering turbulence problem, which comes from the uncertainty of turbulence model, a Bayesian method was developed to identify the parameters for widely used k-ε turbulence model based on the back step flow. The method combines direct computation with finite element method and inverse computation with Metropolis-Hastings sampling algorithm, which can give the posterior distribution of standard k-ε model parameters once the velocity on some observation sites are known. Case computation indicated that after parameter identification the computation has a lower numerical error than that without parameter identification.