This article is devoted to the low Mach number limit of the compressible Oldroyd-B model is rigorously justified in the whole space \(\mathbb {R}^3\) . Under some smallness assumptions on the initial data, we first obtain the global wellposedness of strong solution with uniform regularity with respect to the Mach number. Then, the existence of global strong solution to the corresponding incompressible model is proved via the incompressible limits. Moreover, the convergence rates are also obtained associated with \(L^2\) -norm in the case of well-prepared initial data.
