Over the past two decades, smartphones have become common, and the accompanying devices have also become much more popular and easily accessible worldwide. With the development of smartphones, accompanied by internet facilities, excessive smartphone use or smartphone addiction may cause sleep disturbance and daily dysfunction. This study proposed examining the association between personality traits and smartphone addiction and its effects on sleep disturbance. Four hundred and twenty-two university participants (80 male and 342 female participants) with a mean age of 20.22 years old were recruited in this study. All participants were asked to complete the following questionnaires: Smartphone Addiction Inventory (SPAI), Tri-dimensional personality questionnaire (TPQ), and Chinese Pittsburgh Sleep Questionnaire Index (CPSQI). The results showed that people with a high tendency toward novelty seeking (NS) as a personality trait, compared to those with lower tendency toward NS, are more likely to become addicted to smartphone use. Moreover, those with a stronger trait of being NS and specific impulsivity factor were found to have higher total scores in the SPAI (p < 0.05). In addition, linear regression analysis showed that the individuals with higher scores for withdrawal symptoms on the SPAI and anticipatory worry factor on the TPQ tended to have higher CPSQI total scores (p < 0.05). This information may be useful for prevention in individuals with personality traits making them vulnerable to smartphone addiction and for designing intervention programs to reduce intensive smartphone use and programs to increase capability in managing smartphone use.