An apparatus and method for cell acquisition and downlink synchronization acquisition in an OFDMA wireless communication system are provided. In an SS apparatus in a broadband wireless communication system, a preamble subcarrier acquirer extracts subcarrier values having a preamble code from an FFT signal. A multiplier code-demodulates the subcarrier values by multiplying the subcarrier values by a preamble code. A correlator calculates a plurality of differential correlations in the code-demodulated signal. An IFFT processor IFFT-processes the differential correlations by mapping the differential correlations to subcarriers. A maximum value detector detects a maximum value from the IFFT signal and calculates a timing offset using an IFFT output index having the maximum value.