We propose a polarization demultiplexing method for coherent optical PDM-OFDM based on Stokes space, without inserting training symbols. The proposed approach performs well for different modulation formats of OFDM subcarrier, and shows comparable performances with that of conventional methods, but with a fast convergence speed and reduced overhead. The OFDM signal in the time domain cannot satisfy the conditions of SS-PDM accurately. Therefore, we first digitally convert the received OFDM signals to the frequency domain using fast Fourier transform (FFT). Each subcarrier of the OFDM signal has a much lower speed and narrower bandwidth, the polarization effects that it experiences can be treated as flat. Consequently, we can apply the polarization demultiplexing in Stokes space (SS-PDM) on per subcarrier basis. We verify this method in experiment by transmitting 66.6-Gb/s PDM-OFDM signal with 4QAM subcarrier modulation over 5440km SSMF and 133.3-Gb/s PDM-OFDM signal with 16QAM subcarrier modulation over 960km SSMF respectively. We also compare the results with those of training symbols. Finally, we analyze of the convergence speed of this method.