For a precompact set \(T\) in a Hilbert space and \(\varepsilon >0\), \(N(T,\varepsilon)\) is the minimum number of elements in an \(\varepsilon\)-covering of \(T\). In this paper an estimate of \(N(\text{absconv} (T),\varepsilon)\) is given in terms of \(N(T,\varepsilon)\). Under some regularity conditions the estimate is sharp.