Matrix and its determinant are two basic tools, which are important in financial, accounting, and economic affairs. Therefore, in this paper, a simple and effective method is proposed to obtain the determinant of fuzzy matrices. First, using arithmetic operations based on Transmission Average (TA), the second order fuzzy determinant is calculated. Then, Sarrus rule is defined to calculate third order fuzzy determinant. Finally, by defining minor of fuzzy matrix and ijth adjugate of the fuzzy matrix, nth order fuzzy determinant is calculated. The effectiveness and applicability of the proposed method are verified by solving some numerical examples.