  In this article, we study an initial-boundary-value problem of a coupled
KdV-KdV system on the half line $ \mathbb{R}^+ $ with non-homogeneous boundary
conditions: \begin{equation*} \left\{ \begin{array}{l}
  u_t+v_x+u u_x+v_{xxx}=0, \quad
  v_t+u_x+(vu)_x+u_{xxx}=0, \quad
  u(x,0)=\phi (x),\quad v(x,0)=\psi (x), \quad
  u(0,t)=h_1(t),\quad v(0,t)=h_2(t),\quad v_x(0,t)=h_3(t), \end{array} \right.
\qquad x,\,t>0. \end{equation*} It is shown that the problem is locally
unconditionally well-posed in $H^s(\mathbb{R}^+)\times H^s(\mathbb{R}^+)$ for
$s> -\frac34 $ with initial data $(\phi,\psi)$ in $H^s(\mathbb{R}^+)\times
H^{s}(\mathbb{R}^+)$ and boundary data $(h_1,h_2,h_3) $ in
$H^{\frac{s+1}{3}}(\mathbb{R}^+)\times H^{\frac{s+1}{3}}(\mathbb{R}^+)\times
H^{\frac{s}{3}}(\mathbb{R}^+)$. The approach developed in this paper can also
be applied to study more general KdV-KdV systems posed on the half line.
