This paper presents the results of an investigation into the role of two personality traits (i.e. Agreeableness and Conscientiousness from the Big Five personality traits) in predicting rating error in the self-assessment and peer-assessment of composition writing. The average self/peer-rating errors of 136 Iranian English major undergraduates assigned to two equal-sized groups, one doing self-assessment and the other peer-assessment over nine sessions, were correlated with and regressed against their measures of Agreeableness and Conscientiousness. The results indicated that Agreeableness and Conscientiousness only explained 7% of the variation in self-rating error. Including both Agreeableness and Conscientiousness in a model to predict peer-rating error explained 16% of the variation. When Agreeableness and Conscientiousness were both included in a multiple regression analysis, only Agreeableness was found to significantly predict peer-rating error. Based on these findings, some conclusions are drawn, and pedagogical implications are discussed.