In this paper, we present a fast-converging adaptive frequency-domain minimum-variance-distortionlessresponse (MVDR) beamformer (FMV) for speech enhancement. The well-known FMV solution is optimum in the microphone array processing. However, the direct computation of the optimum FMV solution is often undesirable due to the the inversion of the spatio-spectral correlation matrix which is often unstable and is expensive for large arrays. To avoid the matrix inversion, we develop a fast-converging conjugate gradient (CG) algorithm for iteratively computing the FMV solution. Compared to the existing steepest descent (SD) algorithm, the CG algorithm can dramatically improve the convergence speed for the case of multiple interfering signals in speech enhancement. Therefore, the computational load and processing time can be significantly reduced. The speech enhancement experiments using a four-channel acousticvector- sensor (AVS) microphone array are demonstrated for the target speech signal corrupted by two and five interfering speech signals and superior performance are achieved.