A sparse Electromagnetic Tomography (EMT) system based on Matching Pursuit (MP) algorithms is introduced in this paper. The sparse EMT problem with a linear model is essentially a pursuit for the sparse representation of the spatial conductivity. The framework of sparse representation theory is adopted for the EMT problem. Such notations as spark and mutual-coherence are introduced as tools in the analysis of the recovery results. MP algorithms are considered as effective and efficient solvers towards sparse representation. Some variations of MP are compared in this paper for a random dictionary and the EMT dictionary. The result of conductivity reconstruction proves the effectiveness of MP algorithms for the proposed EMT system.