Interpolation methods are very popular in many practical areas. Sometimes, the data are inaccurate. Namely, we have to do interpolation in an uncertain environment. A feasible method is to represent the quantities as fuzzy numbers. In this paper, the polynomial interpolation of triangular fuzzy numbers is discussed. First, we propose a general form of the polynomial with fuzzy coefficients. Then, the existence of fuzzy interpolating polynomial is shown. Finally, an example illustrates the rationality of the method and the validity of the solution.