In this paper, we propose a rank-reduced Capon algorithm for parameter estimation of near-field sources with uniform linear array. The proposed algorithm can simplify the two-dimensional (2D) peak search within the conventional 2D-Capon algorithm to one-dimensional peak search, which significantly reduces the computational complexity. In addition, the proposed algorithm can obtain automatically paired angle and range estimations of near-field sources, and the parameter estimation performance of the proposed algorithm is very close to the conventional 2D-Capon algorithm. The simulation experiments indicate the effectiveness and superiority of the proposed algorithm.