The recently discovered quasi-one-dimensional (Q1D) superconductor A2Cr3As3 (A=K, Rb, and Cs with TC ≈ 6.1 K, 4.8 K, and 2.2 K, respectively) has intrigued intensive studies. The unconventional superconducting nature has been revealed by both experimental and theoretical investigations. Previously we have carried out neutron diffraction on K2Cr3As3 powder sample and did not observe any signal of static magnetic order. Theoretical calculations have pointed out that K2Cr3As3 is near an in-out co-planar magnetic order and superconductivity is relevant to strong spin fluctuations. We propose to carry out inelastic neutron scattering to probe the low energy magnetic excitations and to identify if there is a spin resonance mode in A2Cr3As3. The proposed neutron study will provide crucial information of its electron pairing mechanism.