Is it possible to file a civil case without court fees

No. You have to pay the court fee if your advocate suggests it.

You cannot file a civil suit without court fee, the court will not entertain any such suit 

Payment of court fees is a subjective topic which has to be specific as per relief(s) claimed therein the suit.

Every suit do required a fixed (ad-valorum) court fees where you are to pay minimal court fees in some reliefs. 

What is the case/ suit being filed and which state you wish to institute the suit as Court fees is a State subject levied as per relief sought by you? 

Under the Court fees Act, 1870, the court fee is mandatory at the time of filing a plaint. The suit will not be numbered or admitted unless proper court fee is paid. The fee depends on the nature of relief (money recovery / declaration / injunction) or value of the suit.

Under order 33 CPC, if you do not have sufficient means, you can apply as an indigent person, you may have to file petition  explaining your financial condition, Schedule of assets. The Court will conduct an inquiry. If the pertition is allowed then you may not have to pay court fee upfront, if you win the court recovers court fee from defendant and if you lose then you may still be liable later. 

Why? Do you lack the means for remitting the Court Fee?

Moreover, what is the subject matter/cause of action? What are the reliefs being sought?  The amount of court fee depends upon the reliefs sought and in many case, it could be nominal.