In this paper, we study the Hyers-Ulam stability of a nonlinear multi-term fractional differential equation with Caputo derivative on bounded time interval. First we discuss the existence and uniqueness for the solutions of initial value problem of a nonlinear multi-term fractional differential equation and second we give a criteria for Hyers-Ulam stability which is our main purpose. The technique relies on the fixed point theorem in the Banach space and the equivalence between Chebyshev norm and Bielecki norm.