  We report $^{75}$As nuclear magnetic resonance (NMR) and nuclear quadrupole
resonance (NQR) studies on the superconductor Rb$_{2}$Cr$_{3}$As$_{3}$ with a
quasi one-dimensional crystal structure. Below $T\sim$ 100 K, the spin-lattice
relaxation rate (1/$T_{1}$) divided by temperature, 1/$T_{1}T$, increases upon
cooling down to $T_{\rm c}$ = 4.8 K, showing a Curie-Weiss-like temperature
dependence. The Knight shift also increases with decreasing temperature. These
results suggest ferromagnetic spin fluctuation. In the superconducting state,
1/$T_{1}$ decreases rapidly below $T_{\text{c}}$ without a Hebel-Slichter peak,
and follows a $T^5$ variation below $T\sim$ 3 K, which point to unconventional
superconductivity with point nodes in the gap function.
