The micromixing combustion technology of hydrogen-enriched natural gas for gas turbines provides robust support for achieving the "dual carbon" goal. Superior fuel-air mixing performance serves as a guarantee for high-efficiency fuel combustion. For a micromixer burner featuring fuel crossflow and air jet flow, novel air-injection hole structures with rounded rectangular shapes were proposed. Numerical simulations were conducted to investigate the influences of characteristic parameters of the air-injection holes on fuel-air mixing performance and pressure loss. The results show that as spacings between two rows of air-injection holes increase, the spatial mixing deficiencies reduce, whereas the variations in pressure loss coefficients are small. As the inclination angles of air jet flow increases, the spatial mixing deficiencies first rise significantly and then tends to a constant value, while the pressure loss coefficients tend to increase with a maximum increment of 0.17%. As the widths of the air-injection hole increase, the spatial mixing deficiencies first decrease and then increase, while the pressure loss coefficients exhibit an increasing trend, reaching a maximum increment of 0.1%. Mechanism analysis reveals that the spatial mixing deficiency is closely associated with the turbulence diffusion and molecular diffusion mechanisms. Meanwhile, the pressure loss coefficients are primarily relevant to the turbulence intensity of the air jets and the local pressure loss caused by the impact of the second row of air jets.