Evolutionary Algorithms are often well-suited for optimization problems. Since mid 1980's, the interest in multi-objective problems has been expanding rapidly. Various evolutionary algorithms for multiobjective problems have been developed which are capable of searching for multiple solutions concurrently in a single run. In this paper, we propose a new genetic symbiosis algorithm (GSA) for multiobjective optimization problems (MOP) based on the symbiotic concept found widely in ecosystems. In the proposed GSA for MOP, a set of symbiotic parameters are introduced to modify the fitness of individuals used for reproduction so as to obtain a variety of Pareto solutions corresponding to user's demands. The symbiotic parameters are trained by minimizing a user defined criterion function. Several numerical simulations are carried out to demonstrate the effectiveness of the proposed GSA.