Numerical simulation of plasma turbulence in the Large Plasma Device (LAPD) [Gekelman et al, Rev. Sci. Inst., 62, 2875, 1991] is presented. The model, implemented in the BOUndary Turbulence (BOUT) code [M. Umansky et al, Contrib. Plasma Phys. 180, 887 (2009)], includes 3-D collisional fluid equations for plasma density, electron parallel momentum, and current continuity, and also includes the effects of ion-neutral collisions. In nonlinear simulations using measured LAPD density profiles but assuming constant temperature profile for simplicity, self-consistent evolution of instabilities and nonlinearly-generated zonal flows results in a saturated turbulent state. Comparisons of these simulations with measurements in LAPD plasmas reveal good qualitative and reasonable quantitative agreement, in particular in frequency spectrum, spatial correlation and amplitude probability distribution function of density fluctuations. For comparison with LAPD measurements, the plasma density profile in simulations is maintained either by direct azimuthal averaging on each time step, or by adding particle source/sink function. The inferred source/sink values are consistent with the estimated ionization source and parallel losses in LAPD. These simulations lay the groundwork for more a comprehensive effort to test fluid turbulence simulation against LAPD data.