The quantum many-body problem for interacting fermions is not without its challenges. Computational methods, [Hartree-Fock (HF), density-functional theory (DFT), quantum Monte Carlo (QMC)] methods have aided greatly in our understanding of systems containing interacting fermions. In this study we explore the possibility of constructing a QMC algorithm based on using the two-body density as the fundamental variable. The fact that the two-body density can be used as a fundamental variable (that is that the energy can be written as a functional of the two-body density, and that minimizing the energy as a functional of the two-body density leads to the ground state energy) can be demonstrated via a simple extension of the proofs for DFT performed originally by Hohenberg and Kohn and later extended to $N$-representable densities by Levy. For the construction of a fermionic QMC algorithm we invoke an auxiliary interacting bosonic system which is required to have the same two-body density as the interacting fermionic system to be investigated (recall that.standard DFT was made into an applicable method via invoking an auxiliary non-interacting system). Such an ansatz leads to an additive correction term in the expression for the ground state energy. We approximate the correction term using Jastrow and Jastrow-Slater type wavefunctions. Since our approximate correction term can be written as an additive two-body and three-body potential, the ground state energy can be evaluated by the standard QMC algorithms for systems of interacting bosons. We perform calculations on $^3$He, and demonstrate that quantitative results can be obtained from our method. In particular our energies show good agreement with other calculations where equivalent levels of approximation were used (fixed-node quantum Monte Carlo without backflow and without three-body correlation). Other properties that we have calculated (potential energy, static structure factor, radial distribution function) are also in good agreement with experiment, and previous calculations. Related Articles: P. Hohenberg and W. Kohn, Phys. Rev. 136B, 864 (1964). W. Kohn and L.~J. Sham, Phys. Rev. 140, A1133 (1965). M. Levy, Proc. Nat. Acad. Sci. USA 76, 6062 (1979). S. Moroni, S. Fantoni, and G. Senatore, Phys. Rev. B 52, 13547 (1995). J. Casulleras and J. Boronat, Phys. Rev. Lett. 84, 3121 (2000).