Medication non-adherence is associated with sub-optimal asthma control. Identification of medical and psychological characteristics associated with non-adherence is important to enable a targeted and personalized approach when working with patients and for the development of interventions to improve patient outcomes by improving medication adherence. We enrolled adults who had diagnosed asthma and who were prescribed daily inhaled corticosteroid medication. We used published and validated instruments to measure medical characteristics including asthma features, practical asthma knowledge and perceived involvement in care and psychological characteristics including anxiety, depression, optimism, and personality traits, to assess the relationship with medication non-adherence. A total of 126 participants provided data, with 64 (50.8%) of the participants identified as non-adherent. Multivariate analyses showed that younger age, high neuroticism scores and a previous asthma hospital admission were associated with non-adherence. Interestingly, depression was associated with a lower risk of non-adherence. This study showed that a personalized medicine approach would include interventions targeting those who are younger, who have been in hospital for asthma and who rate high on the neuroticism personality trait. Given the availability of effective medications for asthma, better understanding of the characteristics associated with non-adherence is important to enhance optimal self-management.