For the dynamic multi-attribute decision-making problem, the decision information is usually given in the form of the interval-valued picture fuzzy number (IVPFN), and the attributes are also usually related to each other, a decision method based on the interval-valued picture fuzzy geometric weighted Heronian average mean (IVPFGWHM) operator is proposed. First, the algorithms of IVPFN are defined by combining the picture fuzzy number (PFN) with the algorithms of the interval-valued intuitionistic fuzzy number (IVIFN). Then, using the algorithms of IVPFN and geometric Heronian average mean operators, four Heronian mean operators for IVPFN are proposed: the interval-valued picture fuzzy geometric Heronian average mean (IVPFGHM) operator, the interval-valued picture fuzzy geometric weighted Heronian average mean (IVPFGWHM) operator, and the dynamic interval-valued picture fuzzy geometric weighted Heronian average mean (DIVPFGWHM) operator. Then some properties of these operators are studied. Furthermore, a multi-attribute decision-making process based on DIVPFGWHM is proposed. At the same time, with the aid of the best-worst method (BWM), we obtained the attribute weights. Finally, by analyzing the current situation of logistics industry and using the proposed method to select logistics companies, and by comparing with the other methods to illustrate the effectiveness and advantages of the developed method.