Based on some fundamental knowledge, research methods and results about the theories of value distribution and normal family for meromorphic functions, and linear algebra, the normality of the families of holomorphic curves is considered. Let $ \mathcal{F} $ be a family of holomorphic maps of a domain $ D\subset \mathbb{C} $ into $ {\mathbb{P}}^{3}\left(\mathbb{C}\right). $ Let $ {H}_{0} $ and $ {H}_{l}\ne {H}_{0} $ be hyperplanes in $ {\mathbb{P}}^{3}\left(\mathbb{C}\right) $ located in general position, where $ l=1,2,\cdots,8 $. Assume the following conditions hold for every $ f\in \mathcal{F}:f\left(z\right) $ belongs to $ {H}_{l} $; if and only if $ \nabla f $ belongs to ${H}_{l} =\{x\in {\mathbb{P}}^{3}\left(\mathbb{C}\right): \langle x, \alpha_l \rangle=0\}$; if $ f\left(z\right) $ belongs to the union set of ${H}_{l}$, then $|\langle f\left(z\right),{H}_{0}\rangle|/ \rhbr \|f\|\|{H}_{0}\|$ is equal or greater than $ \delta $, where $ 0 < \delta < 1 $ is a constant. Then $ \mathcal{F} $ is normal on.