Abstract Professional drivers are at risk of poor well-being, thus, research on how to prevent this status has valuable practical implications. Psychological safety climate, individual perceptions of the safety climate, and time pressure are relevant antecedents of drivers’ well-being. Psychological safety climate acts as a frame of reference for professional drivers because they are remote/lone workers. Time pressure also becomes crucial among drivers who reported higher quantitative job demands and work intensification than employees in other industrial sectors. In addition, several theoretical frameworks suggest that psychological safety climate would minimize time pressure demands, which, in turn, would mediate the relationship between psychological safety climate and drivers’ well-being. Psychological safety climate would diminish time pressure demands because they could be detrimental to safety, in turn, low time pressure demands would be accompanied by an improvement in drivers’ well-being. To date, research on these issues is scarce. This study examines the mediating role of time pressure on the psychological safety climate and drivers’ well-being (general health and lack of burnout) relationship. The sample was composed of 367 professional drivers, and structural equation modeling was used to test two competing models: full and partial mediation. Findings showed that psychological safety climate was negatively associated with time pressure and positively with drivers’ general health and burnout. Time pressure was detrimental to drivers’ well-being, and it partially mediated the relationship between psychological safety climate and drivers’ well-being.