Object-oriented database systems began developing in the mid-80’s out of a necessity to meet the requirements of applications beyond the data processing applications which were [are] served by relational database systems. We propose in this paper a new approach that permits to enrich technique of query optimization existing in the object-oriented databases and the comparative analysis of query optimization for relational databases and object oriented database based on cost, cardinality and no of bytes. Seen the success of query optimization in the relational model, our approach inspires itself of these optimization techniques and enriched it so that they can support the new concepts introduced by the object databases.