Fluid intelligence is a critical factor in learning and instruction. It also influences performance at school and in the workplace. There have been many attempts to directly and indirectly improve general fluid intelligence by training its underlying cognitive functions, such as working memory, cognitive control, or attention. The aim of the present study was to determine the extent to which school-age children's scores on intelligence tests could be improved by attention training. After training sessions, which consisted of four computerized cognitive tasks that practiced various aspects of attention, the children's scores on an attention test improved, with fewer false alarms and increased performance speed. This improvement partially persisted over an extended period of time. However, this effect was not associated with higher intelligence test scores. These results suggest that attention is possible to develop through short-term interventions but general intelligence is not. We interpret our findings in terms of the three-stratum theory of human intelligence.