Kelvin-Helmholtz (K-H) instability triggered by a jet flow along a magnetohydrodynamic (MHD) tangential discontinuity (TD) is studied by means of the two-dimensional MHD simulations. In addition to the vortex structures and the undulant surface waves, we also found fast-mode and slow-mode Mach-cone-like plane waves at the saturation stage of the jet-flow-associated K-H instabilities. Fast-mode Mach-cone-like plane waves are launched in pairs from the ridges of the surface waves when the fast-mode Mach numbers of the surface waves on both sides of the jet flow are greater than one. Slow-mode Mach-cone-like plane waves are found for the first time in a limited range of MSL0y, θ0, and β0, where M SL0y is the slow-mode Mach number of the surface disturbances observed in the ambient plasma rest frame, θ0 is the angle between the surface wave propagation direction and the direction of the ambient magnetic field, and β0 is the plasma β of the ambient plasma. The flaring angle of the fast-mode Mach-cone-like plane wave is less than or equal to 90°, but the flaring angle of the slow-mode Mach-cone-like plane wave is greater than or equal to 90°. A theoretical model is proposed to explain the formation and the characteristics of the slow-mode Mach-cone-like plane waves. The flaring angles of the slow-mode Mach-cone-like plane waves measured from the simulation results are in good agreement with the flaring angles predicted by the theoretical model. Applications of our results to the observations in the space plasma are discussed.