The spectrum of the Van Hove correlation function (CF) is calculated for liquid He(4) at 27 K and a density of 0.25 g/cm(3) by utilizing a recently proposed approximation to quantum CFs derived by combining an effective-frequency Boltzmann-Wigner transform with a linearized path integral expression for CFs. For this anharmonic system and highly nonlinear CF, we obtain excellent agreement with available accurate results. In particular, the first, second, and third moments of the spectrum are in very good agreement with both experiment and earlier theoretical results. Also, the calculated kinetic energy is in excellent agreement with accurate path integral Monte Carlo results.