This research aims to study complex dynamics, where the complex dynamic is considered a branch of dynamical systems, which takes maps from the Riemann sphere to the Riemann sphere. The Julia sets are also examples of fractals and the most important of them, thus being a fractal set. This work aims to study the Julia sets of a family of rational maps are quasicircles and offer the boundaries of the immediate basin of attraction of zero and the infinity are quasi-circles. Now, we introduce the family of  maps are defined as: Gb (z) = 2bn+1 z–n + z2n – b3n+1/zn (z2n – bn–1), (1) where  n ≥ 2  and  b ϵ ℂ\{0} also bn+1 ≠ 1 and b2n+2 ≠ 1.