It is yet to be understood how large-scale environments influence star formation activity in galaxy clusters. One recently proposed mechanism is that galaxy clusters can remain star forming when fed by infalling groups and star-forming galaxies from large-scale structures (LSSs) surrounding them (the "web-feeding" model). Using the COSMOS2020 catalog that has half a million galaxies with high-accuracy (σ _Δz/1+z ∼ 0.01) photometric redshifts, we study the relationship between star formation activities in galaxy clusters and their surrounding environment to test the web-feeding model. We first identify 68 cluster candidates at 0.3 ≤ z ≤ 1.4 with halo masses at 10^13.0–10^14.5 M _⊙ and the surrounding LSSs with the friends-of-friends algorithm. We find that clusters with low fractions of quiescent galaxies tend to be connected with extended LSSs as expected in the web-feeding model. We also investigated the time evolution of the web-feeding trend using the IllustrisTNG cosmological simulation. Even though no clear correlation between the quiescent galaxy fraction of galaxy clusters and the significance of LSSs around them is found in the simulation, we verify that the quiescent galaxy fractions of infallers such as groups (M ₂₀₀ ≥ 10¹² M _⊙) and galaxies (M ₂₀₀ < 10¹² M _⊙) are smaller than the quiescent fraction of cluster members and that infallers can lower the quiescent fraction of clusters. These results imply that cluster-to-cluster variations of quiescent galaxy fraction at z ≤ 1 can at least partially be explained by feeding materials through cosmic webs to clusters.