My very first home purchase is in another state as second home. I have no primary residence but renting. For tax purpose, does my second home is considered as first hom

Your first home means your main home for tax purposes. It is a home where you lived the most.  Your second home is any home that you choose. If you don't rent your very first home, it can be your second home and you can deduct any mortgage interest, real estate tax or mortgage insurance. 

Thanks for your kind response and you are  correct. Still it is not clear to me  here is my situation. I never lived in my second home and still not living but renting it out but that is my first home purchase in other state. I live in different state, currently staying in rental home.  For the  of tax purpose,  could I consider my second home as a first home purchase ( indeed it is my first home purchase ) and take the advantage of first time home buyers tax credit?

IF you are not living in your 2nd home and are renting it out... then it is not considered your first home, it is your rental property. You cannot take the credit... the word "first" is really "main", it has not relevance to the time when the home was purchased. I hope you have found the explanation helpful.