Leaky wave antenna with uniform composite right and left hand (CRLH) transmission line (TL) structure is not suitable for field coverage in wide range space for its high directivity and narrow beam-width. This paper proposed a new kind of leaky wave antennas with non-uniform CRLH TL structure. The propagation constant along the structure varies with the non-uniform parameters, so that the radiation pattern of the leaky wave antenna can be broadened. Two kinds of structures of non-uniform CRLH TLs were studied, and the radiation characteristics of the leaky wave antennas composed of these structures are given.