In high power, medium voltage applications, Current Source Inverters CSIs are connected in parallel to accommodate high DC currents. Using a proper multilevel modulation technique, parallel-connected CSIs can operate as a Multilevel CSI (MCSI). The most common modulation technique for MCSIs is the Phase-Shifted Carrier SPWM (PSC-SPWM). The proper operation of the MCSI requires each CSI modules to have the same average current flowing through its sharing inductors. In practice, the average currents of the CSI modules deviate from their nominal values. Therefore, current balancing mechanisms must be implemented. In the literature, several solutions have been proposed to tackle the current imbalance problem. Most of these solutions are based on altering the phase-shift or magnitude of the carrier waveforms of the PSC-SPWM. They require dedicated PI controllers and they are applicable to MCSIs with specific numbers of levels. This paper proposes a Current Balancing Algorithm (CBA) that can be implemented in any MCSI with any number of levels. The proposed CBA does not require any PI controllers, nor does it require any alteration to the PWM carrier waveforms. The CBA is implemented using a modified Level-Shifted SPWM (LS-PWM). The modified LS-SPWM is shown to produce lower THD and lower di/dt when compared to the PSC-SPWM. The CBA and modified LS-SPWM where implemented in a proof-of-concept lab prototype. The experimental results are presented for the five-level and seven-level cases.