As most of the companions in double neutron star systems should be normal pulsars, the Fast Folding Algorithm (FFA), which is suitable for finding these long spin period pulsars, was used to search their possible radio signals. A time domain resampling code PYSOLATOR was used to maximize the available data length by removing the orbital modulation. We collected and processed 272.2 hr of observational data taken by the Five-hundred-meter Aperture Spherical radio Telescope for the 13 double neutron star systems in its sky. The signal-to-noise ratios of known pulsar signals are obviously improved by this search method, including the detection of a faint pulsar signal which was identified only by folding the data. Unfortunately, no companion signals were found among all the 19,7962 candidates. Geodetic precession of the orbit could enhance detectability in future observations.