In the present work, we make equivalence between non-commutative and Finsler geometries as two useful mathematical tools. Based on this purpose, we were concerned to search this possibility by investigating the massive gravity black holes. Firstly the Lagrangian of system is introduced and then it is rewritten in the non-commutative regime by definition of the new variables. On the other hand, we focus on the Finsler geometry in order to find a Finslerian function which is equivalent with the mentioned non-commutative Lagrangian under special conditions. Also, the effective potential of system was calculated as a part of the corresponding conditions.
