In this paper, we introduce the concept of linear \v{C}ech closure spaces and establish the properties of open sets in linear \v{C}ech closure spaces (L\v{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $\gamma$-open sets, sgc-dense sets and compact sets in L\v{C}CS. We also discuss the concept of relative \v{C}ech closure operator, meet and product linear \v{C}ech closure operators. Lastly, we describe the Moore class on the L\v{C}CS and prove that it is a vector lattice with sufficient properties. Manuscript profile