Aiming　at　solving　the　problems　of　the　conventional　minimum　variance　distortionless　response　(MVDR)　beamformer　in　practical　applications,　such　as　the　sensibility　of　the　steering　vector　mismatch　and　beampattern　distortion,　a　robust　broadband　MVDR　beamforming　method　with　low-latency　by　reconstructing　covariance　matrix　is　proposed　and　applied　to　speech　enhancement　with　a　linear　microphone　array　in　this　paper.　In　this　work,　some　important　steps　are　optimized,　and　the　main　contribution　is　to　consider　the　problem　of　correlation　terms　generated　by　the　low　latency.　Firstly,　the　direction　of　arrival　(DOA)　is　corrected　and　the　steering　vector　is　estimated　based　on　the　sparsity　of　the　DOAs　corresponding　to　the　sound　sources,　which　improves　the　ability　of　anti-mismatches　in　the　steering　vector.　Secondly,　the　correlation　terms　between　the　sound　sources　and　noise　are　estimated　and　eliminated　by　the　Capon　power　within　the　eigen-subspace,　and　the　indirect　dominant　method　is　used　to　eliminate　the　correlation　terms　between　the　sound　sources,　so　that　the　covariance　matrix　is　reconstructed　to　obtain　a　more　robust　MVDR　beamformer.　Thirdly,　the　problem　of　white　noise　amplification　at　low　frequency　bins　is　analyzed,　and　a　white　noise　gain　(WNG)　modification　method　is　proposed　to　obtain　a　compromise　between　the　interference　suppression　and　WNG.　In　the　experiments,　the　TIMIT　corpus　is　used　to　generate　the　multi-channel　speech　data　set,　and　the　performance　of　the　proposed　method　is　evaluated　with　different　DOAs　and　input　signal　to　interference　plus　noise　ratios　(SINRs).　The　experimental　results　show　that　the　proposed　method　can　effectively　suppress　the　interferences　and　reduce　the　noise　with　strong　robustness.　©　2023　Elsevier　Ltd