By using the theories of normal family and value distribution for holomorphic mappings into ${\mathbb{P}^n}\left( \mathbb{C} \right)$, the $n - $dimensional complex projective space, combined with the Zalcman lemma, Landau theorem for holomorphic curves from the unit disk to higher dimensional complex projective space was discussed. Following results can be obtained. Let f be a holomorphic curve of $\Delta $ into ${\mathbb{P}^n}\left( \mathbb{C} \right)$, and let ${D_1},{D_2}, \cdots ,{D_{2t + 1}}$ be 2t+1 hypersurfaces in $t$-subgeneral position in ${\mathbb{P}^n}\left( \mathbb{C} \right)$. If for each $j = 1, 2, \cdots, \rhbr 2t + 1,f\left( \mathbb{C} \right)$ does not take D_j, then absolute constant M exists, such that $\left( {1 - {{\left| z \right|}^2}} \right){f^\# } \leqslant M$, $z \in \Delta$, and ${{T}}(r,f) = O\left( {\log \dfrac{1}{{1 - r}}} \right)$.