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Very recently, the {\it BABAR} Collaboration indicated that there exist anexplicit enhancement structure near 2.2 GeV when focusing on the$e^+e^-\to\pi^+\pi^-$ process again, which inspires our interest in studyingthe production of higher $\rho$ mesonic states. Since the branching ratio of$\pi^+\pi^-$ channel of $D-$wave $\rho$ states are much smaller than $S-$wavestates, we choose $\rho(1900)$ and $\rho(2150)$ as the intermediate states in$e^+e^-\to\pi^+\pi^-$, where $\rho(1900)$ and $\rho(2150)$ are treated as$\rho(3S)$ and $\rho(4S)$ states, respectively. Our result indicates that the$BABAR$'s data of $e^+e^-\to\pi^+\pi^-$ around 2 GeV can be depicted well,which shows that this enhancement structure near 2.2 GeV existing in$e^+e^-\to\pi^+\pi^-$ can be due to the contribution from two $\rho$ mesons,$\rho(1900)$ and $\rho(2150)$. Additionally, this conclusion can be enforced bythe consistence of the extracted values of$\Gamma_{e^+e^-}\mathcal{B}(\pi^+\pi^-)$ of $\rho(1900)$ and $\rho(2150)$ inthe whole fitting processes and the corresponding theoretical calculations. Thepresent study of $e^+e^-\to\pi^+\pi^-$ data may provide valuable information toestablish the $\rho$ meson family.

Toward $e^+e^-\to \pi^+\pi^-$ annihilation inspired by higher $\rho$ mesonic states around 2.2 GeV