  In this article, we study an initial-boundary-value problem of the sixth
order Boussinesq equation on a half line with nonhomogeneous boundary
conditions: \[ u_{tt}-u_{xx}+\beta u_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=0,\quad
x>0\mbox{, }t>0,\] \[u(x,0)=\varphi (x), u_t(x,0)=\psi ''(x),\] \[
u(0,t)=h_1(t), u_{xx}(0,t)=h_2(t), u_{xxxx}(0,t)=h_3(t),\] where $\beta=\pm1$.
It is shown that the problem is locally well-posed in $H^s(\mathbb{R}^+)$ for
$-\frac12<s\leq 0$ with initial condition $(\varphi,\psi)\in
H^s(\mathbb{R}^+)\times H^{s-1}(\mathbb{R}^+)$ and boundary condition
$(h_1,h_2,h_3) $ in the product space $H^{\frac{s+1}{3}}(\mathbb{R}^+)\times
H^{\frac{s-1}{3}}(\mathbb{R}^+)\times H^{\frac{s-3}{3}}(\mathbb{R}^+)$.
