A new grating leaky wave antenna based on left-handed material was proposed and its radiation characteristics were carefully and rigorously analyzed by using a method which combined the rigorous mode matching procedure with multimode network method. The variations of the leakage constant with structure parameters were given in this study to show the special properties of this kind of antenna. The numerical results indicate that the new leaky wave antenna has much larger leakage constant than that of conventional one. The reason for this phenomenon is discussed.