Matrices play significant roles in various areas in science and engineering. The problems involving various types of uncertainties cannot be solved by the classical matrix theory. Neutrosophic sets theory was proposed by Florentin Smarandache in 1999, where each element had three associated essential functions, namely the membership function (T), the non-membership (F) function and the indeterminacy function (I) defined on the universe of discourse X, the three functions are entirely independent. In this paper, the interval-valued neutrosophic fuzzy matrix (IVNFM) is introduced. Some fundamental operations are also presented. The need of the interval-valued neutrosophic fuzzy matrix (IVNFM) is explained by an illustration. Illumination of some of the operators are given with the help of the example.