IC 10 X-1 is one of the close X-ray binaries containing a Wolf–Rayet donor, which can provide an evolutionary link between high-mass X-ray binaries and gravitational wave sources. It is still unclear about the precise nature of the accreting compact object in IC 10 X-1, although it looks more like a black hole (BH) than a neutron star. In this work, we use a binary population synthesis method to simulate the formation of IC 10 X-1–like binaries by assuming different common-envelope ejection efficiencies. This work represents a big step forward over previous studies since we adopt new criteria for mass-transfer stability. These criteria allow the formation of IC 10 X-1–like systems without experiencing common envelope evolution. Based on our calculations, we propose that the compact object in IC 10 X-1 is a BH with a mass of ∼10–30 M
⊙ and the progenitor evolution of this binary probably just experienced stable mass transfer.