We describe Monte Carlo simulations of a model for diffusion with trapping on a percolation lattice, which is a limiting case of models for diffusion of water in glassy polymers. In this model, particles walk randomly on a hypercubic lattice. The lattice is decorated with black (polymer) and white (nonpolymer) sites in a realization of the percolation model. The particles hop on and off of white sites without constraint as in a random walk, but if they step onto a black site they are trapped forever. Double occupancy of any site is forbidden and the simulations are done at finite diffusant density by effectively fixing a chemical potential. In our two-dimensional simulations, the particles are fed into the system from one side and a front of trapped particles advances into the lattice. At low densities, the first moment of the trapped-particle density obeys the scaling form expected for diffusion on the percolation model, but the value of the conductivity exponent is significantly different. We find =1.5 0.1 rather than the reported value of 1.3 for diffusion on realizations of the percolation lattice.