A high rate age-momentum correlation spectroscopy apparatus for a variable-energy positron beam has been developed at the Electrotechnical Laboratory. An intense slow positron beam generated by an electron linear accelerator is used for the apparatus. In order to obtain a high coincidence count rate, we have optimized the pulse stretching condition of the positron beam. Furthermore, high rate pre-amplifier and amplifier have been installed for the Ge solid-state detector. Using the now AMOC apparatus, the maximum coincidence count rate of more than 1,000 cps has been achieved.