Processing speed is considered a key cognitive resource and it has a crucial role in all types of cognitive performance. Some researchers have hypothesised the importance of white matter integrity in the brain for processing speed; however, the relationship at the whole-brain level between white matter volume (WMV) and processing speed relevant to the modality or problem used in the task has never been clearly evaluated in healthy people. In this study, we used various tests of processing speed and Voxel-Based Morphometry (VBM) analyses, it is involves a voxel-wise comparison of the local volume of gray and white, to assess the relationship between processing speed and regional WMV (rWMV). We examined the association between processing speed and WMV in 887 healthy young adults (504 men and 383 women; mean age, 20.7 years, SD, 1.85). We performed three different multiple regression analyses: we evaluated rWMV associated with individual differences in the simple processing speed task, word-colour and colour-word tasks (processing speed tasks with words) and the simple arithmetic task, after adjusting for age and sex. The results showed a positive relationship at the whole-brain level between rWMV and processing speed performance. In contrast, the processing speed performance did not correlate with rWMV in any of the regions examined. Our results support the idea that WMV is associated globally with processing speed performance regardless of the type of processing speed task.