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We study the time evolution of holographic subregion complexity (HSC) inVaidya spacetime with dS boundary. The subregion on the boundary is chosen tobe a sphere within the cosmological horizon. It is found that the behaviour ofHSC is similar to that in cases with flat boundary. The whole evolution can bedivided into four stages: First, it grows almost linearly, then the growthslows down; After reaching a maximum it drops down quickly and gets tosaturation finally. The linear growth rate in the first stage is found todepend almost only on the the mass parameter. As the subregion size approachesthe cosmological horizon, this stage is expected to last forever with thesubsequent three stages washed out. The saturation time $\tilde{t}_{sat}$depends almost only on the subregion size $\tilde{R}$ as $\tilde{t}_{sat} =\tanh^{-1} (\tilde{R})$ which is linear in $\tilde{R}$ when $\tilde{R}$ issmall but logarithmically divergent as $\tilde{R}$ approaches the cosmologicalhorizon.

Subregion complexity in holographic thermalization with dS boundary