We are concerned with the multi-dimensional compressible viscoelastic flows of Oldroyd type. In order to capture the damping effect of the additional deformation tensor, to the best of our knowledge, the “div-curl” conditions play a key role in previous efforts. Our aim is to remove the structural conditions and establish a global existence of strong solutions to compressible viscoelastic flows in critical spaces. In absence of compatible conditions, the new effective flux is introduced, which enables us to capture the dissipation arising from combination of density and deformation tensor. The partial dissipation in non-Newtonian compressible fluids is weaker than that of classical Navier-Stokes equations. This is a collaborative work with Xinghong Pan and Yi Zhu.