This paper investigates the scheduling problem of dealing with disruption caused by machine breakdown under the environment of identical parallel machines. When a machine breakdown changes the scheduling environment, the original schedule cannot be executed according to the prescribed plan. The objective after disruption is to create a recovery schedule that minimizes the original objective function and the deviation from the original schedule. The original objective function is the total weighted completion time, and the deviation is the completion time of jobs from the planned one. The recovery scheduling problem is formulated as an integer programming model. A Lagrangian relaxation (LR) framework that relaxes the machine capacity constraints is proposed for solving the model. The subgradient method is used to update the values of Lagrangian multipliers. The extensive computational experiments are carried out, and the numerical results demonstrate that the proposed LR approach based oil the developed model can provide an excellent recovery schedule Solution in a timely manner.