We propose a variant of Orthogonal Matching Pursuit (OMP), called LoCOMP, for scalable sparse signal approximation. The algorithm is designed for shift- invariant signal dictionaries with localized atoms, such as time-frequency dictionaries, and achieves approximation performance comparable to OMP at a computational cost similar to Matching Pursuit. Numerical experiments with a large audio signal show that, compared to OMP and Gradient Pursuit, the proposed algorithm runs in over 500 less time while leaving the approximation error almost unchanged.