In connection with the development of a new family of high-pressure HPC with ultra-high pressure ratio and the number of stages 10–11, a special attention should be paid to the development of the first high-load stage, because compressor performance directly depends on its excellence. Despite the fact that the stage at nominal rotational speeds can have optimal performance, stall margins at intermediate rotational speeds can decrease because of a sizable IGV closure. One of the ways to increase stall margins is the use of labyrinth-type casing treatments. The Stage “A-1” studied in this work is a full-scale first stage in a six-stage high-pressure compressor (HPC) for a core demonstrator. The primary design task for the labyrinth-type casing treatment (CT) is to keep performance at design rotational speeds (n = 100%) or improve them, if possible, and increase stall margins at intermediate speeds (n = 70% and n = 80%). The labyrinth-type CT consisting of 3 circumferential grooves located above the middle of the blade chord projection is specially designed and manufactured for this stage. Our computations show that the use of the labyrinth-type CT leads to a shift of performance towards higher airflow and efficiency that is a good agreement with experimental data. An increase in stall margins without changes in efficiency is found by calculations, whereas the test, on the contrary, shows no influence on stall margins and an increase in efficiency by ∼1.5% (the same as at rated speeds). Both investigated turbulence models (SST and k-ε) do not provide good agreement with the experimental data. The SST model captures CT influence, but decreases stall margin. The k-ε model show agreement with the test in stall margin, but cannot capture CT influence. In addition, both models show lower efficiency compared with the experimental data. To verify the NUMECA Fine Turbo (version 11.1) mathematical model and numerical method, calculated and experimental characteristics of the Stage A-1 with a smooth flow passage and a labyrinth-type CT are compared. The NUMECA Autogrid 5 grid generator is used to build the grid.