This paper investigates the Dynamic Multi-attribute Decision Making (DMADM) problems, in which all the attribute values provided by decision maker at different periods take the form of intuitionistic trapezoidal fuzzy numbers. A new operator called dynamic intuitionistic trapezoidal fuzzy weighted geometric averaging (DITFWGA) operator is presented. A model based on DITFWGA operator is developed to deal with DMADM problems. The intuitionistic trapezoidal fuzzy weighted geometric averaging (ITFWGA) operator is utilized to aggregate the overall intuitionistic trapezoidal fuzzy information corresponding to each alternative, and then rank the alternatives and select the best one. Finally, an illustrative example is given to verify the developed approach and demonstrate its practicality and effectiveness.