This paper considers the hedging problem for a class of stochastic differential delay equations with Markov switching.When the price process of a risky asset follows the considered model,we derive a martingale representation for the price process of a contingent claim written on the risky asset with respect to an equivalent martingale measure obtained by the Esscher transform.Then,under some conditions for the coefficients of the model,we identify the continuous-time hedging strategy by minimizing the residual risk in the incomplete market due to the additional source of uncertainty introduced by the regime switching.