Is it okay to go solo in research? I am a PhD student third year and I almost finished working on a research with my supervisor. I have few research problems in my mind, I told him about one or two but he did not paid that much attention. I want to try one or two research problem on my own. I am little hesitant to ask him about this. Am I suppose to work with him on each research problem during my PhD? 
I don't know what will be his reaction. What you people will suggest me to do? I strongly believe that I can do it. There is no funding problem. Second part of the question is  how to increase the chances of that the research I will on my own will be accepted in some conference ( definitely I can take some help from my supervisor )
There are two components to this question. "Is it okay to work on my own 'independent' project in a PhD?"

Yes, definitely. The purpose of a PhD is to train an independent researcher. An advisor who feeds their student the tasks or jobs to do throughout their PhD is probably doing them a disservice, as they would not have the opportunity to learn how to devise and carry out their own independent research projects. Being in the third year, you have probably finished your classes and accrued enough research experience to do so. Of course it is expected that you keep your advisor in the loop if you do decide to work on such a side project.

Now, with regards to "What would my advisor think if I worked on my own 'independent' project?"

That depends entirely on the advisor and your funding situation. If you are full supported by a specific grant, it is probably a bad idea to work on an unrelated topic. Ideally, you should work the problem into something which can be related to the grant. Of course, if you are self-funded or have a no strings attached fellowship, things can be more flexible for you.