As an extension of intuitionistic fuzzy sets, picture fuzzy sets can deal with vague, uncertain, incomplete and inconsistent information. The similarity measure is an important technique to distinguish two objects. In this study, a similarity measure between picture fuzzy sets based on relationship matrix is proposed. The new similarity measure satisfies the axiomatic definition of similarity measure. It can be testified from a numerical experiment that the new similarity measure is more effective. Finally, we apply the proposed similarity measure to multiple-attribute decision making.