In this paper, we propose the concept of Suzuki type fuzzy Z-contractive mappings, which is a generalization of Fuzzy Z-contractive mappings initiated in the article [S. Shukla, D. Gopal, W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets and Systems 350 (2018)85-95]. For this type of contractions suitable conditions are framed to ensure the existence of fixed point in G-complete as well as M-complete fuzzy metric spaces. A comprehensive set of examples are furnished to demonstrate the validity of the obtained results.