Mode structures of drift-wave instabilities modified by a field-aligned flow velocity shear are investigated, where axial and azimuthal wave numbers are measured using Y-shaped and Γ-shaped electrostatic probes, respectively. When the ion flow velocity shear is produced by applying different bias voltages to three segments of an ion source, drift waves having azimuthal mode number m = 1, 2, and 3 are observed to be excited simultaneously. It is found that the excitation-threshold value of the shear strength depends on the azimuthal mode number, as expected from a model based on a kinetic theory, suggesting that the observations are explained by the competition between inverse electron Landau damping and shear-modified ion Landau damping.