Let $G=(V,E)$ be a finite and simple graph with $\lambda_1, \lambda_2, …, \lambda_n$ as its eigenvalues. The Estrada index of $G$ is $EE(G)=\sum_{i=1}^{n}e^{\lambda_{i}}$. For a positive integer $k$, a connected graph $G$ is called strict $k$-quasi tree if there exists a set $U$ of vertices of size $k$ such that $G\setminus U$ is a tree and this is as small as possible with this property. In this paper, we define point attaching strict $k$-quasi tree graphs and obtain the graph with minimum Estrada index among point attaching strict $k$-quasi tree graphs with $k$ even cycles.