  This paper studies distributional chaos in non-autonomous discrete systems
generated by given sequences of maps in metric spaces. In the case that the
metric space is compact, it is shown that a system is Li-Yorke{\delta}-chaotic
if and only if it is distributionally{\delta}'-chaotic in a sequence; and three
criteria of distributional {\delta}-chaos are established, which are caused by
topologically weak mixing, asymptotic average shadowing property, and some
expanding condition, respectively, where {\delta} and {\delta}' are positive
constants. In a general case, a criterion of distributional chaos in a sequence
induced by a Xiong chaotic set is established.
