In this paper, we present an Ornstein-Zernike-type integral equation applicable to quantum fluids. This integral equation was obtained by averaging fully imaginary-time-dependent reference interaction site model integral equation for the quantum fluids over imaginary time. The resulting integral equation is a scalar integral equation for linear response correlation function. The self-correlation function in the integral equation was determined in a self-consistent manner with the aid of Feynman's variational perturbation method. Our theoretical treatment is an extension of the theory for an excess electron in the classical solvents [J. Chem. Phys. 81, 1975 (1984)] to that for the fully quantum fluids. Numerical calculations have been performed for the fluid helium-4 assuming Boltzmann statistics. The calculated pair correlation functions are in good agreement with path integral molecular dynamics results. The experimental static structure factors are well described by our theory. It was found that the calculated excess quantum kinetic energy decreases slowly with raising temperature; even at high temperature the quantum effect on the kinetic energy cannot be neglected.