Abstract We have developed an FX-architecture digital spectro-correlator for the Atacama Compact Array of the Atacama Large Millimeter/submillimeter Array. The correlator is able to simultaneously process four pairs of dual polarization signals with a bandwidth of 2 GHz, which are received by up to sixteen antennas. It can calculate auto- and cross-correlation spectra, including cross-polarization in all combinations of all the antennas, and output correlation spectra with flexible spectral configuration, such as multiple frequency ranges and multiple frequency resolutions. Its spectral dynamic range is estimated to be higher than 10$^{4}$ relative to $T_{\rm sys}$ from processing results of thermal noise for eight hours with a typical correlator configuration. The sensitivity loss is also confirmed to be 0.9% with the same configuration. In this paper, we report on the detailed design of the correlator and the verification results of the developed hardware.