Abstract: Based on von Karman length scale and new Reynolds stress constitutive relation, the k-equation was closed and the turbulence dissipation term was modeled by algebraic method. On the basis of KDO (kinetic dependent only) model, a compressible von Karman length scale was introduced to obtain a new turbulence model CKDO (compressible kinetic dependent only) for complex compressible flow. There were no empirical coefficients in the CKDO model and only two tunable parameters were derived from the refinement of the boundary layer. The results of the numerical simulations of RAE2822 airfoil, axisymmetric bump pipeline and ONERA-M6 wing transonic flow show that the CKDO turbulence model agrees well with the experimental data for the pressure coefficient simulation of the flow field. It is shown that the CKDO model can simulate the transonic flow field more accurately.