An automated version of the Verlet neighbor list algorithm in which the optimum neighbor list radius (SKIN) increases with the system size (N) shows an almost linear CPU time versus N dependence over the range 10(2) < N < 10(4). The algorithm's speed is comparable to that of a Link-Cell code (Grest et al., 1989), and much higher than that achieved by using "recommended" values for the neighbor list radius and update frequency, especially for large systems.