Quantum spin liquid is an exotic state without magnetic order down to zero-temperature due to spin frustration, which is closely related to high temperature superconductivity. Therefore, an important issue arises whether the quantum spin liquid can be adjusted into a superconductor, even high-T_c superconductor, by using pressure or chemical doping. Rear-earth chalcogenides NaYbCh₂ (Ch = O, S, Se), consisting of planar triangular lattice, exhibit no long-range magnetic order down to the lowest measured temperatures in specific heat, nuclear magnetic resonance, and neutron scattering, and are considered as a quantum spin liquid candidate. Here we investigate the electrical transport properties of NaYbCh₂ (Ch = O, S, Se) under high pressures. For NaYbSe₂, zero-resistance behavior is observed at 26.9 GPa, showing that the superconductivity comes into being. The superconducting transition temperature (T_c) is around 5.6 K at 26.9 GPa and robust against pressure till 45 GPa. The phase diagram of T_c versus pressure for NaYbSe₂ is constructed. For NaYbS₂, the room temperature resistance decreases from the order of 10¹¹ Ω at 10 GPa to 10 Ω at 67 GPa. However, neither superconductivity nor insulator-metal transition is observed. Additionally, the NaYbO₂ keeps insulating and the resistance is too large to be detected in a pressure range of 0–60 GPa.