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This paper deals with a multi closed-loop adaptive neuro-fuzzy inference system (ANFIS) design for the under-actuated quadrotor systems. First, the training data set for the fuzzy inference system is obtained using a proportional integral derivative controller. Then, an initial ANFIS controller is designed, where the integral control action is preserved in the multi-closed-cloop ANFIS for each quadrotor system state. Thereafter, scaling gains are added to the controller inputs/outputs, and a multidimensional PSO algorithm is used to tune all the control parameters. Besides, using a simulation example, the aerial vehicle performances are investigated in the presence of an unknown payload mass parameter. Specifically, the position tracking performances of the proposed multi closed-loop PSObased ANFIS plus integral control strategy is compared with the classical PID, conventional ANFIS, and non-optimized ANFIS plus integral controllers. Thus, using the conducted simulation results, it results that the multi closed-loop PSO-based ANFIS plus integral can achieve perfect translational trajectory-tracking and ensure better attitude stabilization despite unknown quadrotor payload mass parameter. Therefore, the proposed new multi closed-loop PSO-based control strategy may be considered as an efficient controller when considering an arbitrary trajectory-tracking problem for the quadrotor system.