This paper presents a low-complexity MUSIC-like algorithm with sparse linear array. Three uniform linear arrays are combined into a sparse linear array. An extended signal subspace is got by organizing the forth-order-cumulant of array received data. During this process, no eigen-value decomposition (EVD) or singular-value decomposition needs to be implemented. Then, a MUSIC-like method is proposed to estimate the direction-of-arrival of incident signals. In order to bring down the computational complexity further, an ESPRIT-like algorithm is used to obtain the initial estimations of direction angles, by which the search range can be diminished significantly. Compared with the classical MUSIC and PM, the proposed MUSIC-like algorithm shows better angular resolution and higher estimation accuracy. Moreover, because of the avoidance of EVD and the reduction of search range, the computational burden of the proposed MUSIC-like algorithm with per-estimation by ESPRIT-like algorithm is small. The performance of the proposed method is demonstrated through numerical simulations.