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In this paper, the author's present one algorithm of algebraic PWM strategy for nine - level Neutral Point Clamping (NPC) Voltage Source Inverter (VSI) is presented. This algorithm uses a control model of the inverter developed previously by the authors. In the first part, we develop a working model of this inverter, without presumption on its control, by using the connection functions of this converter. In the second part the control models of this converter by using respectively instantaneous and generating connection functions are reviewed. In the last part, one algebraic PWM control strategy of the inverter is proposed. The obtained results are full of promise to use this digital strategy to control nine-level NPC VSI used in high voltage, high power applications as electrical traction.