Summary: In this paper, the solution to fuzzy fractional initial value problem [FFIVP] under Caputo-type fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhara difference and strongly generalized fuzzy differentiability. The modified fractional Euler method based on a generalized Taylor’s formula and a modified trapezoidal rule is used for solving initial value problem under fuzzy fractional differential equation of order \(\beta \in (0,1)\). Solving two examples of linear and nonlinear FFIVP illustrates the method.