The linear sampling method (LSM) is an effective method to detect complicated structures in a short time. In this paper, we develop a novel kind of LSM by means of metamaterial (MTM) leaky wave antennas (LWAs) to conduct spectrally-encoded three-dimensional (3D) microwave tomography that can reconstruct a conductive target with coaxial multi-layer and various diameter cylinders. The unique frequency-space mapping feature of MTM LWAs enables an efficient 3D microwave imaging with a larger field of view compared with conventional LSM approaches that usually operate at one single frequency. Validated through both theoretical analysis and experimental results, the proposed MTM imaging scheme allows us to reconstruct 3D shapes effectively with minimal prior knowledge of the target and computational resources. Furthermore, the measured results verify the proposed imaging method by successfully detecting the unknown targets with different shapes and locations for the MTM LWAs operating at 1.8-3 GHz.