Consider complex projective space $\Bbb CP^n$. Then define $$L = \{ (\ell, z) \in \Bbb CP^n\times \Bbb C^{n+1} \mid z \in \ell \}.$$Then $L$ is a complex line bundle over $\Bbb CP^n$. The projection is the obvious one and it is clear that each fibre is a vector space of dimension $1$. Then we're left to check the local trivialization postulate.
I'm not so used to work with projective spaces, so I was trying to write $L$ as a pull-back of any another bundle, to no avail. Maybe defining trivializations is not so hard after all, but I guess that trying to write $L$ as a pull-back is an interesting question on its own... so, any ideas? Thanks.