Let $\phi$ be a smooth pluri-subharmonic solution to (6.1), (6.2) in $B_{1}(0)\subset\mathbb{C}^{n}$, such that $\Delta\phi\in L^{p}(B_{1}(0))$ and $\sum_{i}\frac{1}{\phi_{i\bar{i}}}\in L^{p}(B_{1}(0))$ for some $p>3n(n-1)$. Then there exists a constant $C_{6}$, depending only on $p$, $||\Delta\phi||_{L^{p}(B_{1}(0))}$, $||\sum_{i}\frac{1}{\phi_{i\bar{i}}}||_{L^{p}(B_{1}(0))}$, such that $\frac{1}{C_{6}}\leq\phi_{i\bar{j}}\leq C_{6}$, $|\nabla G|\leq C_{6}$ in $B_{\frac{1}{2}}(0)$.