Based on the ESPRIT-like and polynomial rooting methods, a high-performance and low computational cost localization algorithm for the mixed near-field sources (NFS) and far-field sources (FFS) is proposed using the uniform linear sensor array. First, we combine the steering vectors of the two subarrays to eliminate the range parameters and then yield a new steering vector, which only contains direction-of-arrival (DOA) information. Second, based on the ESPRIT-like and polynomial rooting methods, the DOAs of all NFSs and FFSs are obtained from the new steering vector. Third, with the DOA estimates, the range parameters are estimated depending on the polynomial rooting method again; and further according to the number of the closest to the unit circle roots, we can determine the number of sources at the same DOA direction. Finally, based on the size of the range parameters, the types (NFS or FFS) of sources can be confirmed. In addition, the proposed algorithm does not require the high-order statistics or any 1- or 2-D search and thus has low computational cost. Meanwhile, it makes full use of the array aperture and obtains outstanding estimation performance for both the DOA and range parameters. Moreover, the proposed algorithm avoids parameter match procedure. Numerical experiments show the performance of the proposed algorithm in this paper.