In this paper, the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta fractional difference.Every Δ steps, the state variable is instantly modified with the same impulse value, chosen from a bifurcation diagram versus impulse. It is shown that the solution of the impulsive control is bounded. The numerical results are verified via time series, histograms and the 0-1 test. Several examples are considered.