The purpose of this paper is to Provide conditions for the existence of farthest points of closed and bounded subsets of Hilbert operator spaces. This will done by applying the concept of numerical range. We give, inter alia, some results to characterize farthest points of a subset of a C * -algebra A from a fixed element x ∈ A. Meanwhile, we point out the main theorems of R. Saravanan and R. Vijayaragavan [11] are incorrect, by given two counterexamples.