Hertz contact is a ideal contact status which supposes the contact surfaces as not moving,completely smooth and no lubricant,but real surfaces of meshing gears are rude,exiting relative motion and lubricating,and which is a kind of nonHertz contact. Based on EHL theory,this paper proposes a new gear design theory and method,called gear design theory and method of non-Hertz contact. The new theory and method comprehensive considers every factors of influencing strength and lubrication of gears,and which can ensure the designed gears meet the dual requirements of strength and elastic hydrodynamic lubrication. Specific formulas of are given out and a large number of engineering examples are used to verify the new theory and method proposed in the paper,and the results show that the conformity of new design theory and method and the actual engineering examples are very well,and which can directly apply to practical engineering design to meet the requirement of engineering design. In particular,to design of high speed and heavy duty gear transmission,the new theory and method of this paper has important theoretical significance and practical value.