The recently superconductivity in a quasi-one-dimensional (Q1D) crystal structure, A2Cr3As3 (R=K, Rb and Cs), have been intensively investigated both experimentally and theoretically. We have published one musr paper on K2Cr3As3 PRB(2015) and second is in preparation. The new compounds ACr3As3 (A = K, Rb and Cs) remain 1D (Cr3As3)∞ linear chains, and the interchain distance can be tuned by the incorporation of the alkali-metal cations with different sizes. The physical-property indicates 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. Using the high sensitivity of the ZF-μSR and LF-SR technique, we would like to find the static or dynamic magnetism in these compounds.