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Some methods can be used to solve a Dual Fully Fuzzy Linear System (DFFLS). The use of the method that produces accurate and efficient solutions is the main choice. Jacobi Method is the approximate method used to solve a dual fully fuzzy involving the arithmetic concept of a triangular fuzzy number.  The process of the Jacobi Method is started by inputting the initial value to obtain a solution with a relatively small error. This purpose requires that the equations of the system must be diagonally dominant. The solution obtained from a dual fully fuzzy linear system by Jacobi Method is a single solution that has a minimum error. This article will give an algorithm and its implementation in the Mathematica program to obtain an effective and efficient solution using the Jacobi method.