Most part of my result is as same as orginal version. Can I make a paper?
Normally extensions to existing work are valuable. I suggest that you take advice from your advisor if there is any to give. 

But you can also write it up and submit it to a journal. Let the editors and reviewers decide whether it is worth publication. It would be a mistake to just assume that it isn't without feedback from other mathematicians - such as reviewers. 

This is true since, as you say, the original proof doesn't work for higher dimensions and the original authors may not have contemplated the extension.