Hi, is VOA office open on 16th-20th June 2015? Is there possible any visa rejection on that day?

Which VOA office did you refer to? Shenzhen or Zhuhai? The five-day special VOA and three-day VOA is available to the citizens of certain countries. If you haven't been to mainland China before, I am afraid that you may not be able to acquire it.

By the way, it has nothing to do with timing. No matter when you apply, there is still a possibility that you might be refused.