We study the growth of cosmological perturbations in the model of Lorentz-violating massive gravity . The Friedman equation in this model acquires an unconventional term due to the Lorentz-breaking condensates which has the equation of state w = -1 / ( 3 \gamma ) with \gamma being a free parameter taking values outside of the range [ 0 , 1 / 3 ] . Apart from the standard contributions , the perturbations above the Friedmann background contain an extra piece which is proportional to an arbitrary function \vartheta ( x ^ { i } ) of the space coordinates . This function appears as an integration constant and corresponds to a non-propagating scalar mode which may , however , become dynamical with the account of the higher-derivative corrections . For -1 < \gamma < 0 and \gamma = 1 the “ anomalous ” perturbations grow slower than the standard ones and thus the model is compatible with observations . Whether the model is experimentally acceptable at other values of \gamma depends on the value of the function \vartheta ( x ^ { i } ) at the beginning of the radiation-dominated epoch .