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We study the following nonlinear Hartree-type equation \begin{equation*}-\Delta u+V(x)u-a(\frac{1}{|x|^\gamma}\ast |u|^2)u=\lambdau,~\text{in}~\mathbb{R}^N, \end{equation*} where $a>0$, $N\geq3$,$\gamma\in(0,2)$ and $V(x)$ is an external potential. We first study theasymptotic behavior of the ground state of equation for $V(x)\equiv1$, $a=1$and $\lambda=0$ as $\gamma\nearrow2$. Then we consider the case of sometrapping potential $V(x)$, and show that all the mass of ground statesconcentrate at a global minimum point of $V(x)$ as $\gamma\nearrow2$, whichleads to symmetry breaking. Moreover, the concentration rate for maximum pointsof ground states will be given.

Concentration Behavior of Nonlinear Hartree-type Equation with almost Mass Critical Exponent