Superconductivity in crystals without inversion symmetry has received extensive attention due to its unconventional pairing and possible nontrivial topological properties. Using first-principles calculations, we systemically study the electronic structure of noncentrosymmetric superconductors $A_2$Cr$_3$As$_3$ ($A$=Na, K, Rb and Cs). Topologically protected triply degenerate points connected by one-dimensional arcs appear along the $C_{3}$ axis, coexisting with strong ferromagnetic (FM) fluctuations in the non-superconducting state. Within random phase approximation, our calculations show that strong enhancements of spin fluctuations are present in K$_2$Cr$_3$As$_3$ and Rb$_2$Cr$_3$As$_3$, and are substantially reduced in Na$_2$Cr$_3$As$_3$ and Cs$_2$Cr$_3$As$_3$. Symmetry analysis of spin-orbit coupling $g_{k}$ suggests that the arc surface states might remain stable in the superconducting state, giving rise to possible nontrivial topological properties.
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