We report As-75 nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) studies on the superconductor Rb2Cr3As3 with a quasi-one-dimensional crystal structure. Below T similar to 100 K, the spin-lattice relaxation rate (1/T-1) divided by temperature, 1/T1T, increases upon cooling down to T-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-c without a Hebel-Slichter peak, and follows a T-5 variation below T similar to 3 K, which points to unconventional superconductivity with point nodes in the gap function.