We propose a direct-detection receiver capable of detecting polarization-division-multiplexed (PDM) ON-OFF keying (OOK) signals without using a dynamic polarization controller. The proposed receiver, consisted of a polarization-beam splitter, three 1 x 2 directional couplers, three photodetectors, three analog-to-digital converters, and a digital signal processing unit, can discriminate among the four symbol combinations of the PDM-OOK signal with the help of a short training sequence. For a demonstration, we show that the proposed receiver can detect a 20-Gb/s PDM-OOK signal even when its polarization is scrambled at the speed of 3 Mrad/s.