A hybrid optimization approach that combines a well know global optimization method genetic algorithm (GA) sequenced by a speed efficient gradient based local optimization algorithm sequential quadratic programming (SQP) has been applied to design of small solid propellant launch vehicle (LV) configured in tandem stages. The proposed LV design uses the same solid rocket motor (SRM) for the first and second stages, with different convergent nozzle module adapted to the external pressure and flight altitude of each stage, while the third stage was designed and optimized to reach the established mission. The mission considered herein consists in sending a small payload of 100 kg to a low earth orbit (LEO) of 600 km oriented to modular nano and microsatellites. For this purpose, a multidisciplinary optimization approach based on the multi-discipline feasible framework had been implemented in Matlab, that includes the propulsion, mass, aerodynamic and trajectory modules. The application of hybrid optimization algorithm based on a GA-SQP in design of a small solid propellant LV demonstrates the validity of the used approach reaching the established mission satisfying all optimization constraints