Matthew Stibbe's advice targeted geeks writing for a general audience, but it applies to grant writers as well. From one of my favorite writers about writing:
Geeks: How to Write for a Non-Technical Audience : "Bad Language" : Thinkmap Visual Thesaurus
User testing. I recommend three kinds of testing: read the article aloud to yourself. Does it sound like you? Is it natural? Does it make sense? Ask a non-technical friend or colleague to read it and check that they picked up on the main points you wanted to convey. Finally, try to find someone who can proofread it properly- it's very hard to proofread your own work.