To address the issue of phase mismatch, mainlobe broadening, image defocusing, and high computational complexity caused by spherical wavefront propagation in near-field imaging of uniform linear array (ULA) imaging sonar, this paper proposes an interpolation-free near-field frequency-domain beamforming algorithm for uniform linear arrays. Under the considered operating conditions, the exact range history is approximated as the sum of a range-dependent quadratic term and a range-independent linear term with respect to the element position. The quadratic term produces negligible envelope migration; therefore, only its phase needs to be compensated. By contrast, the linear term produces more significant range migration, which is corrected together with its associated phase through range-domain and azimuth-domain FFT processing. Under the adopted range-history approximation and discrete sampling conditions, this implementation avoids the explicit point-by-point fractional-delay interpolation required by the backprojection (BP) algorithm. The proposed method substantially reduces the computational cost while maintaining near-field focusing performance comparable to that of the BP algorithm. For the simulated data, the runtime is reduced from 58.23 s to 0.41 s, with only a 0.1% broadening of the azimuth impulse-response width and a 0.11 dB degradation in the peak sidelobe ratio. For the measured lake-trial data, the runtime is reduced from 50.18 s to 0.29 s.