The quality and loss of products are crucial factors separating competitive companies in global market. Firms widely employ a loss function to measure the loss caused by a deviation of the quality variable from the target value. Monitoring this deviation from the process target value is important from the view of Taguchi's philosophy. In practice, there are many situations where the interested data distribution may be or not be normal. This paper aims at developing a new loss control chart for monitoring process loss center under non-normal distributions. We proposed an unbiased new average run length (ARL) to measure the detection performance of the proposed loss control chart. The numerical approach of calculating feasible control limits with unbiased ARL of the loss control chart is developed. Numerical results demonstrate the reasonable and reliable out-of-control detection performance of the proposed new ARL-unbiased loss control chart. We recommend applying the proposed ARL-unbiased loss control chart to monitor the loss center for non-normal quality variable.