This paper is concerned with nonlinear stability of rarefaction wave to the Cauchy problem for a blood flow model, which describes the motion of blood through axi-symmetric compliant vessels. Inspired by the stability analysis of classical $p$-system, we show the solution of this typical model tends time-asymptotically toward the rarefaction wave under some suitably small conditions and there are more difficulties in the proof due to the appearance of strong nonlinear terms including second-order derivative of $v$ with respect to the spatial variable $x$. The main result is proved by employing the elementary $L^2$ energy methods. This is the first result about nonlinear stability of some nontrivial profiles (i.e., non-constant function patterns) for the blood flow model.