A stable and accurate algorithm for simulating massive damped Brownian moti
on is proposed and discussed. The algorithm, being fully integral for the f
riction and noise terms and predictor-corrector for the potential force in
the Langevin equations, is stable upon changing time step and for various m
asses of the particle. In particular, the limit of zero inertia can be safe
ly taken, and the algorithm yields naturally the corresponding overdamped c
ase. The steady velocity of a particle moving in a titled periodic potentia
l is calculated and three algorithms are compared.