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Applying the discrete supplementary variables method, matrix-geometric solution and quasi birth-death technique, we investigate a discrete time Geo/Geo/1 queue system with negative customer, Bernoulli feedback and multiple working vacations. Firstly, by applying the discrete supplementary variable technique, we give the transition probability matrix of this complex system. Secondly, using the matrix-geometric solution and quasi birth-death technique and solving equation sets, we get the equilibrium distributions for the number of customers, the average number of customers and the stochastic decomposition of the steady-state queue length. Finally, by presenting the numerical examples, we make some two-dimensinal graphs, which help us to intuitively analyze the influence of parameters on the system performance. [ABSTRACT FROM AUTHOR]