We demonstrate an optical transmission system based on a 6-level PSK modulation format and differential detection with a partial symbol delay. The 6-level PSK signal is simply generated by using a chirp-free Mach-Zehnder modulator followed by a phase modulator. In order to convert the phase information of the 6-level PSK signal into the intensity, we utilize a pair of two Mach-Zehnder delay-line interferometers with having a differential delay less than the symbol duration of the signal unlike a conventional differential detection scheme. We evaluate the performances of the differential 6-level PSK signal and compare them with that of a conventional DQPSK signal. In addition, the transmission performance of the 21.4-Gb/s 6-level PSK signal is experimentally verified in a 240-km long dispersion-managed fiber link. Furthermore, additional simulation results show that the tolerance to optical filtering and chromatic dispersion of the 107-Gb/s differential 6-level PSK signal is improved significantly by adopting the partial demodulation scheme.