Abstract: In this study, the prediction accuracy on long-term of future behavior in a 3-D chaotic map is possible. This study introduces and justifies by numerical simulation a new phenomenon shown by the 3-D map which is the behavior in the 3-D map is always regular and periodic and bounded on large time, i.e. that the behavior repeats itself regularly after cycles on large time intervals. The new 3-D map produces new several chaotic attractors obtained via quasi-periodic route to chaos.