In this study, the occurrence conditions of rockbursts induced by broken hard and thick rock strata (HTRS) in fully mechanized longwall face are investigated by dividing the surrounding rock of a roadway rib into three zones: burst-resistance zone (BRZ), burst-inoculation zone, and stable zone. On this basis, the process of impact vibration energy (released by the broken HTRS) transformation in these zones was analyzed, and theoretical equations are presented to calculate the strain energy, dissipated energy and shock vibration energy. In addition, an energy criterion associated with the critical broken length of the HTRS, the width of burst-resistance zone, and the burst proneness index was proposed to predict rockbursts induced by broken HTRS in fully mechanized longwall face. Moreover, to control these types of rockbursts effectively, a quantitative method was proposed for determining the limit broken length of the HTRS and the BRZ. The research results show that the energy criterion may forecast these typical rockbursts, and rockburst hazards can be eliminated using the proposed method.