We have performed molecular dynamics simulations of amorphous Si3N4 containing boron (Si-B-N). We have examined short-range atomic arrangements and self-diffusion constants of amorphous Si-B-N systems with various boron contents. Our simulations show that boron atoms are threefold coordinated by nitrogen atoms and that nitrogen atoms are bonded to both silicon and boron atoms in the amorphous network of Si-B-N. Also, the self-diffusion constant of nitrogen in Si-B-N is much decreased compared with that in amorphous Si3N4. This suggests that boron is important in decreasing the mobility of atoms in amorphous Si-B-N, which may explain the improved thermal stability of amorphous Si-B-N relative to amorphous Si3N4 observed experimentally.