Delta robots have been successfully researched and manufactured in many countries. In this paper, the authors will research and compare many different controllers to control the delta robot so that it works stability when changing the working speed and load. The regression fuzzy neural network along with PID controller (RFNNC-PID) is used to observe the output error parameters of the robot through the identifier to update and adjust the optimal input parameters to control the robot, contributing error reduction of the closed-loop control system. The advantage of this controller is that it does not care about the robot's mathematical model and the RFNNC-PID controller has been successfully simulated by the authors in MATLAB/Simulink through the robot's trajectory control. The proposed controller will be compared to the single neuron PID controller and the traditional PID controller in MATLAB/Simulink. The simulation results show that the proposed controller is better than the single neuron PID controller and the traditional one with obtaining response time about 3.8 ± 0.1 (s) and without steady-state error.