We start with the compressible Oldroyd-B model derived in[2](J.W.Bar-rett,Y.Lu,and E.Süli,Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model,Commun.Math.Sci.,15(2017),1265-1323),where the existence of global-in-time finite-energy weak solutions was shown in two dimen-sional setting with stress diffusion.In the paper,we investigate the case without stress diffusion.We first restrict ourselves to the corotational setting as in[28](P.L.Li-ons,and N.Masmoudi,Global solutions for some Oldroyd models of non-Newtonian flows,Chin.Ann.Math.,Ser.B,21(2)(2000),131-146)We further assume the extra stress tensor is a scalar matrix and we derive a simplified model which takes a similar form as the multi-component compressible Navier-Stokes equations,where,however,the pressure term related to the scalar extra stress tensor has the opposite sign.By employing the techniques developed in[30,35],we can still prove the global-in-time existence of finite energy weak solutions in two or three dimensions,without the pres-ence of stress diffusion.