We investigate the superconducting-gap anisotropy in one of the recently discovered BiS_{2}-based superconductors, NdO_{0.71}F_{0.29}BiS_{2} (T_{c}∼5 K), using laser-based angle-resolved photoemission spectroscopy. Whereas the previously discovered high-T_{c} superconductors such as copper oxides and iron-based superconductors, which are believed to have unconventional superconducting mechanisms, have 3d electrons in their conduction bands, the conduction band of BiS_{2}-based superconductors mainly consists of Bi 6p electrons, and, hence, the conventional superconducting mechanism might be expected. Contrary to this expectation, we observe a strongly anisotropic superconducting gap. This result strongly suggests that the pairing mechanism for NdO_{0.71}F_{0.29}BiS_{2} is an unconventional one and we attribute the observed anisotropy to competitive or cooperative multiple paring interactions.