Don't be written off!

One of the most basic skills needed to succeed, or even survive, in professional life is to be able to write well. This is true whether you work in science, industry, business, or an NGO.
Of course, there are exceptions where an individual is incredibly gifted at the technical side of a job and can't even write a coherent paragraph. But, sorry, that individual is probably not you! Furthermore, even they need a collaborator or manager who is good at writing.

Most young scientists struggle to write a paper or a grant application, particularly when English is not their first language.

Here are a few suggestions on how to improve your writing skills over time.

First, accept that writing is hard work. Even John Grisham says that!

Accept that developing your writing skills is a project of a lifetime. This means starting early.

If you are an undergrad, take some humanities courses that require writing essays. Take writing lab reports seriously.
If you have to write a thesis, start writing it now.
Take a writing course. Take another.

Practise.
Write papers yourself. If you are the first author you really should write the first draft, including the introduction yourself. Don't let your boss (or someone more experienced) do it or expect them to. Your draft may be poor and get heavily edited or even discarded completely. But you will learn from the process and with time confidence and competence will follow.
Write a blog, even if no one reads it.

Learn by osmosis.
Read scientific authors known for the clarity and beauty of their writing. eg. David Mermin and Roald Hoffmann.
Read a lot and read broadly publications (newspapers and magazines) that are known for their excellent writing: The New York Times, The Economist, The New Yorker,...
Read famous novels and non-fiction books.

Read slowly and thoughtfully. Don't just skim everything.
I also suspect you may be better off reading hard copies.
Try to notice whether a piece of writing: makes sense, is hard to understand, is enjoyable to read?

Any other suggestions?