Number of conventional methods are available for solving different types of optimization problems. But due to their complexity and convergence problems these methods are not able to give optimal solution. A gear transmission problem is one of the most complex optimization problems because of relationship between different variables. A Gear design require the designer to compromise many design variables; i.e. continuous, discrete & integer variables in order to determine best performance of gear set. Therefore researchers are now going to use Evolutionary Techniques. Genetic Algorithm (GA) is one of such technique. In this paper the attempt has been made to optimize worm and worm wheel with multiple objectives, which takes gear ratio (i), face width of worm & worm wheel (b) and pitch circle diameters of worm (dw) & worm wheel (dg) as design variables. The main objective function is to minimize volume of worm and worm wheel and remaining objectives are taken as constraints such as centre distance, deflection of worm and beam strength of worm gear.