In this paper, we are interested in the following planar Choquard equation \begin{equation*} \begin{cases} -Δu=\displaystyle\left(\int\limits_Ω\frac{u^{p+1}(y)}{|x-y|^α}dy\right)u^{p},\quad u>0,\ \ &\mbox{in}\ Ω, \quad \ \ u=0, \ \ &\mbox{on}\ \partial Ω, \end{cases} \end{equation*} where $Ω$ is a smooth bounded domain in $\mathbb{R}^2$, $α\in (0,2)$ and $p>1$ is a positive parameter. Unlike the higher-dimensional case, we prove that the least energy solutions $u_{p}$ neither blow up nor vanish, and develop only one peak as $p\to+\infty$ under suitable assumptions on $Ω$. In contrast, the modified solutions $pu_p$ exhibit blow-up behavior analogous to that observed in higher dimensions. Furthermore, as $α\to 0$, the main results of this paper become consistent with the known conclusions for the corresponding Lane-Emden equation.
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