Let $H=\{0,1,2\}$ and consider the Cayley table \[ \begin{array}{c|ccc} \cas &0 &1 &2\\ \hline \vspace{0.01em} 0&\{0\}&\{0\}&\{0\}\\ 1&\{0,1,2\}&\{0,1\}&\{0,1\}\\ 2&\{0,2\}&\{0,1,2\}&\{0,2\} \end{array} \] By routine calculations, we see that $(H;\cas,0)$ satisfies all the properties of a hyper BCI-algebra except the requirement that $x \ll y$ and $y \ll x$ implies $x=y$. Notice in the table that if $x=0$ and $y=1$, we have $0\ll1$ and $1 \ll 0$ but $0\neq 1$. But a closer inspection suggests that this hyperalgebra satisfies the property $((x \cas y)\cas z)\ll (y \cas z),~\forall x,y,z\in H$. This leads to the conceptualization of hyper GR-algebras which is an ongoing study done by G. Petalcorin and R. Indangan. \\ \vspace{0.5em} Let $H$ be a nonempty set and $\cas$ be a hyperoperation on $H$. Then $(H; \cas,0)$ is called a $hyper~GR-algebra$, if it contains a constant $0\in H$ and satisfies the following conditions, for all $x,y,z\in H$:\\ $(HGR_1):~((x\cas z)\cas (y\cas z)) \ll (x\cas y);$\\ $(HGR_2):~(x\cas y)\cas z = (x\cas z) \cas y;$\\ $(HRG_3):~x \ll x;$\\ $(HGR_4):~(0\cas (0 \cas x)) \ll x, x \neq 0$; and\\ $(HGR_5):~((x \cas y))\cas z \ll (y \cas z)$.\\ \vspace{0.5em} This paper will deal on hyper homomorphism and some of its properties on hyper GR-algebra.