Passive suspension system is used in most vehicles due to its low energy consumption and low cost in most vehicles. Therefore, today there is a challenge in order to enhance the suspension system. The aim of this study is to present a new method for Multi-Objective design of vehicle suspension based on the use of asymmetrical dampers (Nonlinear). Hence, It is shown that using these type of dampers with a choice of two type coefficient by which one of them is in compression and another one in expansion, will lead to a more optimal design compared to those in the literature. For this purpose, vehicle was modeled using full model with eleven degree of freedom under random road excitation. Then, since the tasks of suspension system are reduction of vertical acceleration exerted on passengers, reduction of pitch acceleration of sprung mass, improving road holding and reduction of the change of four wheel work space. Therefore, the problem is defined as a Multi-Objective problem with conflicting objectives which formulated and solved by NSGA-II algorithm. The obtained results indicated that using asymmetrical dampers leads to more efficient design compared to those methods with symmetrical dampers.