Following the definition of fuzzy normed linear space which was introduced by Bag and Samanta in general t-norm settings, in this paper,  definition of fuzzy strong $\phi$-b-normed linear space is given. Here the scalar function $|c| $ is replaced by a general function $ \phi(c) $ where $ \phi $ satisfies some properties. Some basic results on finite dimensional  fuzzy strong $\phi$-b-normed linear space are studied.