This paper is dedicated to the Cauchy problem of the incompressible Oldroyd-B model with general coupling constant $\omega\in(0,1)$. It is shown that this set of equations admits a unique global solution in a certain hybrid Besov spaces for small initial data in $\dot{H}^S\cap\dot{B}^{d/2}_{2,1}$ with $-\frac d2<s<\frac d2-1$. In particular, if $d\geq3$, and taking $s=0$, then $\dot{H}^0\cap\dot{B}^{d/2}_{2,1}=\dot{B}^{d/2}_{2,1}$. Since $B^t_{2,\infty}\hookrightarrow B^{d/2}_{2,1}$ if $t>\frac d2$, this result extends the work by Chen and Miao [Nonlinear Anal. 68 (2008), 1928--1939].