The picture fuzzy multiple attribute decision making methods are based on unknown attribute weights, and mostly only consider objective attribute information. To overcome these defects, a picture fuzzy LINMAP multiple attribute decision making method based on the regret theory is developed, in which the decision maker's regret aversion behavior and the influence relationships among attributes are considered. Firstly, a picture fuzzy regret-rejoice function is defined on the basis of the regret theory and the computational formula of perceived utility value is given. Secondly, the picture fuzzy preference information set is proposed to represent the interaction between attributes, and the picture fuzzy consistency and inconsistency between pair-wise rankings of alternatives and the preference information assumed apriori given by decision makers are proposed. Thirdly, the objective function with parameters is established by the picture fuzzy score function and accuracy function, and the picture fuzzy threshold is designed so that inconsistent degree is minimized and the difference between the consistent degree and inconsistent degree is at least not less than the proposed picture fuzzy threshold. Base on this, a new optimization model is established to solve the weights and fuzzy ideal points of different attributes of each alternative, and then the perceived utility values of each alternative are calculated and the alternatives are ranked also. Finally, the rationality of the developed method is illustrated by an example, and the flexibility and merits of the proposed method are demonstrated by sensitivity analysis and comparative analysis.