In the kneading of glass-fiber-reinforced plastics by twin-screw extrusion, the use of a backward-mixing screw (BMS) element for melt mixing has been found to be effective in dispersing glass-fiber bundles. In this study, we use the computational fluid dynamics (CFD) to study the mechanism of dispersion by a BMS element for glass fiber bundles. The result of CFD for a BMS and a forward kneading disk (FKD) reveals that the melt mixing by a BMS is highly effective to act the required stress on overall resin. In addition, there is a good correlation between the incidence of undispersed glass-fiber bundles measured experimentally and the minimum value of distribution of the time-integrated stress calculated numerically. On the basis of the above results, we propose a method to predict the operating conditions in which the incident probability of undispersed glass-fiber bundles and thermal degradation are controlled.