Using a nonlocal time-dependent theory of convection, we have calculated the linear non-adiabatic oscillations of the Horizontal Branch (HB) stars, with both the dynamic and thermodynamic coupling between convection and oscillations been carefully treated. Turbulent pressure and turbulent viscosity have been included consistently in our equations of non-adiabatic pulsation. When the coupling between convection and oscillations is ignored, for all models with Te ≤ 7350K, the fundamental through the second overtone are pulsationally unstable; while for Te ≤ 6200K all the models are unstable up to (at least) the 9th overtone. When the coupling between convection and oscillations is included, the RR Lyrae instability strip is very well predicted. Within the strip most models are pulsationally unstable only for the fundamental and the first few overtones. Turbulent viscosity is an important damping mechanism. Being exclusively distinct from the luminous red variables (long period variables), the HB stars to the right of the RR Lyrae strip are pulsationally stable for the fundamental and low-order overtones, but become unstable for some of the high-order overtones. This may provide a valuable clue for the short period, low amplitude red variables found outside the red edge of the RR Lyrae strip on the H-R diagram of globular clusters. Moreover, we present a new radiation modulated excitation mechanism functioning in radiation flux gradient regions. The effects of nonlocal convection and the dynamic coupling between convection and oscillations are discussed. The spatial oscillations of the thermal variables in the pulsational calculations have been effectively suppressed.