This paper presents a new idea to solve the selective harmonic elimination (SHE) equations with non equal dc sources using Hybrid Newton Raphson Method (HNRM). This technique is a combination of genetic algorithm (GA) and Newton Raphson Method (NRM). The HNRM technique effectively eliminates the lower order harmonics from the output voltage of the converter. In this paper, it has been also shown that, if the notch angles determined for equal dc sources are used for unequal dc sources then the content of lower order harmonics increases, as a result of this voltage THD also increases. Simulation results of 11-level cascaded multilevel inverter with unequal dc sources are shown and the effects of variation of input dc voltage on output voltage THD of the converter are presented. The proposed technique effectively calculates the optimum value of switching angles with variation in input dc bus voltage over the entire range of modulation index.