Let $X,Y$ be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping $f:X\to Y$ satisfies $$\begin{array}{c}\hfill f(x+iy)+f(x-iy)=2f\left(x\right)-2f\left(y\right)\end{array}$$ for all $x$, $y\in X$, then the mapping $f:X\to Y$ satisfies $f(x+y)+f(x-y)=2f\left(x\right)+2f\left(y\right)$ for all $x$, $y\in X$. Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation () in complex Banach spaces. In this paper, we will adopt the idea of Park and Th. M. Rassias to prove the stability of a quadratic functional equation with complex involution via fixed point method.