Let $(X_n)$ be a strictly stationary sequence with a marginal distribution function $F$ such that $1-F(x)=x^{-\alpha}L(x)$, $x>0$, where $\alpha>0$ and $L(x)$ is a slowly varying function. We assume that only observations of $(Xn)$ are available at certain points. Under assumption of weak dependency we proved the consistency of Hill's estimator of the tail index a based on an incomplete sample from $\{X_1,X_2,\dots,X_n\}$. This is an extension of the results of Hsing [15] and Mladenović and Piterbarg [19].