One of the important methods in many practical areas is interpolation method. Clearly, in many real world problems, the input and output data are involved with uncertainty. So, we must develop interpolation methods for fuzzy data. In this paper, first, we define a new set of spline functions to interpolate given fuzzy data. Then we discuss some important theorems on these splines together with their existence and uniqueness properties. Also, we present numerical examples to illustrate the differences between using our spline and other interpolations that have been studied before.