Histone deacetylases play an important role in regulating gene expression by modifying histones and changing chromatin conformation. HDAC dysregulation is involved in many diseases, such as cancer, autoimmune and neurodegenerative diseases. Histone deacetylase 1 (HDAC1) inhibitors represent an important class of drugs. Quantitative Structure-Activity Relationship (QSAR) classification models were developed using 2D RDKit molecular descriptors; ECPF4 (Extended Connectivity Fingerprint) circular fingerprints; and the Random Forest, Gradient Boosting, and Support Vector Machine methods. The developed models were integrated into the HDAC1 PREDICTOR application, which is freely available at the link https://ovttiras-hdac1-inhibitors-hdac1-predictor-app-z3mrbr.streamlitapp.com. The HDAC1 PREDICTOR web application allows one to reveal the compounds for which the predicted activity to inhibit HDAC1 is higher than that of the reference Vorinostat compound (IC50 = 11.08 nM). The algorithm implemented in HDAC1 PREDICTOR for determining the contributions of molecular fragments to the inhibitory activity can be used to find the molecule segments that increase or decrease the activity, enabling the researcher to conduct a rational molecular design of new highly active HDAC1 inhibitors. The developed QSAR models and the code for their construction in the Python programming language are freely available on the GitHub platform at https://github.com/ovttiras/HDAC1-inhibitors.