We investigate the superconducting-gap anisotropy in one of the recently discovered BiS$_2$-based superconductors, NdO$_{0.71}$F$_{0.29}$BiS$_2$ ($T_c$ $\sim$ 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 6$p$ 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 unconventional one and we attribute the observed anisotropy to competitive or cooperative multiple paring interactions.