A new approach to the sensorless speed control of six-phase induction machine (6PIM) using an Adaptive Neural Fuzzy Inference Systems (ANFIS) as a rotor speed estimator to avoid mechanical sensor is proposed in this paper. The ANFIS is first trained offline to estimate the rotor speed in a wide range of operation and then implemented online to perform the field-oriented control (FOC) of the 6PIM. Fuzzy-PI (FPI) controllers are associated to FOC to control the rotor speed and the stator currents. For this, the input-output scale factors of the FPI systems are determined using Genetic Algorithms (GA). Experimental results assess the feasibility of the proposed method with high accuracy and good dynamic behavior in speed estimation and control of the 6PIM.