In this paper we introduce a new class Gλ(F) of sequence of fuzzy numbers. It is a subclass of Gλ(F), the space of all entire sequence of fuzzy numbers. The completeness and some topological properties of Gλ(F) are discussed. Also it is proved that Gλ(F) is a Banach space and it has monotone metric. Some matrix transformations involving this space are obtained.