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. The related new compounds ACr3As3 (A = K, Rb and Cs) also have 1D (Cr3As3)∞ linear chains, and the interchain distance can be tuned by the incorporation of the alkali-metal cations with different sizes. The susceptibility measurements indicate a local-moment behaviour (T>60K), and the moments freeze into a cluster spin-glass state below 5~6 K. No superconductivity was observed in ACr3As3 materials, with increasing the interchain distance, the Cr effective moments increase monotonically. We propose to use inelastic neutron scattering to study the spin excitations in these compounds.