The conceptions called non-inferior Nash strategies for linear quadratic multi-team differential games are introduced. The necessary and sufficient conditions for its existence are derived. The second objective within each team is investigated in the preconditions of Nash competition between the teams and of cooperation within each team. A static game between the teams for their cooperative weight vectors within each team is established, and the optimal weight vectors of satisfying the equilibrium for the second objectives between the teams are obtained. The open-loop non-inferior Nash strategies of satisfying the non-inferior optimum for the first objective and the equilibrium between the teams for the second objective are developed. Finally, an economic game example in two team systems is presented to illustrate the effectiveness of the strategy.