The aim of this study was to examine the effects of the motivational climate created by the coach and perceived by a group of young, high-performance handball players on their fear of failure and precompetitive anxiety. The study participants were 479 young handball players. The age range was 16–17 years old. Players were administered a battery composed of a Perceived Motivational Climate in Sport Questionnaire, a Performance Failure Appraisal Inventory, and Competitive State Anxiety Inventory-2R, to measure the aforementioned theoretical constructs. Using structural equation modelling (SEM), the results showed that the handball players experienced high levels task-involving climate and moderate values of self-confidence. In contrast, players experienced lower levels of ego-involving climate, fear of failure, and cognitive and somatic anxiety. The obtained model shows that fear of failure positively mediates the association between an ego-involving climate with both cognitive and somatic anxiety, and negatively in terms of self-confidence. In contrast, fear of failure does not mediate the associations between a task-involving climate and both somatic and cognitive anxiety and self-confidence.