An ultracold Fermi gas with a zero-range attractive potential in the unitary limit is investigated using variational and diffusion Monte Carlo methods. Previous calculations have used a finite-range interaction and extrapolate the results to zero-range. Here we extend the quantum Monte Carlo method to directly use a zero-range interaction without the need of an extrapolation. We employ a trial wave function with the correct boundary conditions and modify the sampling procedures to handle the zero-range interaction. The results are reliable and have low variance.