Is making data/file compression program using c++ language feasible? Suggest!?

Yes. C++ is a Turing-complete language- anything a computer can do can be written in C++. If you're not a very experienced developer, you might want to look at Huffman encoding. It's a pretty simple and reasonably effective compression algorithm. It's used for compression in both PNG and zip files (in combination with another, more complex algorithm called LZ77).