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Electrical submersible pumps (ESPs) are multistage centrifugal pumps driven by specially designed three-phase induction motors. They are used in many applications such as nuclear and petroleum industries. In the presented paper, we study the speed control of an ESP pump using a rule-based fuzzy logic controller (FLC). As a case study, an oil well is considered to analyze the effects of changing the speed of an ESP pump on both the ESP pump and motor parameters. The proposed speed control model of ESP pumps provides the ability to optimize wells production and power consumption, as well as soft starting of ESP motors. This is done by using a variable speed drive (VSD), which changes the frequency of the voltage supplied to the ESP motor. The utilized VSD model consists of a two-level voltage source inverter (VSI), space vector pulse width modulator (SVPWM) and a rule-based fuzzy logic speed controller. Also, in this study a dynamic hydraulic model of an oil well is implemented. In this study, a mathematical model of the ESP motor and ESP pump is developed. The obtained simulation results show that the combination of the FLC speed Controller and SVPWM provides a faster and more effective method of controlling the speed of electrical submersible pumps than the conventional PID speed controllers. The MATLAB/ SIMULINK software is used to achieve simulative validation of the complete system.