Due to the lack of target speech annotations in real-recorded far-field conversational datasets, speech enhancement (SE) models are typically trained on simulated data. However, the trained models often perform poorly in real-world conditions, hindering their application in far-field speech recognition. To address the issue, we (a) propose direct sound estimation (DSE) to estimate the oracle direct sound of real-recorded data for SE; and (b) present a novel pseudo-supervised learning method, SuPseudo, which leverages DSE-estimates as pseudo-labels and enables SE models to directly learn from and adapt to real-recorded data, thereby improving their generalization capability. Furthermore, an SE model called FARNET is designed to fully utilize SuPseudo. Experiments on the MISP2023 corpus demonstrate the effectiveness of SuPseudo, and our system significantly outperforms the previous state-of-the-art. A demo of our method can be found at https://EeLLJ.github.io/SuPseudo/.