Frequency-domain equalization (FDE) has been studied for suppressing inter-symbol interference (ISI) due to frequency selective fading in single carrier systems. When a high-mobility terminal is assumed in the system, channel transition within an FDE block cannot be ignored. The ISI reduction performance of FDE degrades since the cyclicity of the channel matrix is lost. To solve this problem, a method of dividing the received data block into multiple subblocks has been proposed, where pseudo cyclic prefix (CP) processing is introduced to realize periodicity in each subblock. In this method, the performance is degraded by the inherently-inaccurate pseudo CP. In this paper, we study the application of frequency-domain turbo equalization (FDTE) to subblock processing for improving the accuracy of pseudo CP. The simulation results show that FDTE with subblock processing yields remarkable performance improvements.