How to include industrial research experience legally? I am planning to apply for Ph.D. after spending the last couple of years in Industry.

Problem is, the project I was working on (in this company) though completed, may not have my name as author. As per company policy, as I am leaving before it is getting published.

So, is there any way (or is it legal) I can include the project, in my CV without giving many details?
So, is there any way (or is it legal) I can include the project, in my CV without giving many details? 


If supplying this information is prohibited by a nondisclosure agreement you signed with your employer, then there's nothing you can do.  It won't help your case at all to say "I did something really interesting, but I can't tell you anything about it, so you'll just have to believe me."

Assuming your employer doesn't object to providing this information, you can say anything you like in your CV, as long as it's true.


  Problem is, the project I was working on (in this company) though completed, may not have my name as author. As per company policy, as I am leaving before it is getting published.


This is indeed the problem.  By academic standards, leaving the company before a completed project is published should have no impact whatsoever on authorship.  If you won't be an author, then either you are being treated unfairly/unethically, or you never deserved to be an author in the first place.  That's a tricky situation that readers won't be able to sort out without more information.

So although you can include such a project on your CV, just listing it there probably won't help you much because nobody will know what to make of it.  If the project really matters for your application, then you'll need to explain in much more detail in your statement of purpose.