The collapse and fragmentation of primordial filamentary clouds under isotropic dissociation radiation was investigated with one-dimensional hydrodynamical calculations. We investigate the effect of the dissociation photon on the filamentary clouds by calculating non-equilibrium chemical reactions. With the external radiation assumed to turn on when the filamentary cloud forms, a filamentary cloud with low initial density ($n_0$$\le$ 10$^{2}\ $ cm$^{-3}$ ) suffers a photodissociation of hydrogen molecules. In such a case, since the main coolant is lost, the temperature increases adiabatically enough to suppress the collapse. As a result, the filamentary cloud fragments into very massive clouds ($\sim$ 10$^{5}\ M_\odot$ ). On the other hand, the evolution of the filamentary clouds with high initial density ($n_0$$>$ 10$^{2}\ $ cm$^{-3}$ ) is hardly affected by the external radiation. This is because the filamentary cloud with high initial density shields itself from the external radiation. It is found that the fragment mass increases owing to the external radiation. This result is consistent with previous results with one-zone models. It is also found that the fragment mass decreases owing to the external dissociation radiation in the case with a sufficiently large line mass.