This paper describes an algorithm that enhances speech by independent vector analysis (IVA) using harmonic frequency dependency for robust speech recognition. While the conventional IVA exploits the full-band uniform dependencies of each source signal, a harmonic clique model is introduced to improve the enhancement performance by modeling strong dependencies among multiples of fundamental frequencies. An IVA-based learning algorithm is derived to consider the non-holonomic constraint and the minimal distortion principle to reduce the unavoidable distortion of IVA, and the minimum power distortionless response beamformer is used as a pre-processing step. In addition, the algorithm compares the log-spectral features of the enhanced speech and observed noisy speech to identify time–frequency segments corrupted by noise and restores those with the cluster-based missing feature reconstruction technique. Experimental results demonstrate that the proposed method enhances recognition performance significantly in noisy environments, especially with competing interference.