An apparatus for transmitting broadcast signals includes an encoder to encode service data, a framing block to map the encoded service data into data symbols to build at least one signal frame, a frequency interleaver to frequency interleaving data in the at least one signal frame by using an interleaving sequence, a modulator to perform a modulation on the frequency interleaved data by the OFDM (Orthogonal Frequency Division Multiplex) scheme and a transmitter to transmit the broadcast signals having the modulated data. A different interleaving sequence is used for two consecutive data symbols corresponding to an OFDM symbol pair or a data symbol corresponding to an OFDM symbol according to an FFT size of the modulation.