Abstract: Motivated by 1 and 2, we study in this paper the optimal (from the insurer's point of view) reinsurance problem when risk is measured by a general risk measure, namely the GlueVaR distortion risk measures which is firstly proposed by 3.Suppose an insurer is exposed to the risk and decides to buy a reinsurance contract written on the total claim amounts basis, i.e. the reinsurer covers and the cedent covers . In addition, the insurer is obligated to compensate the reinsurer for undertaking the risk by paying the reinsurance premium, ( is the safety loading), under the expectation premium principle. Based on a technique used in 2, this paper derives the optimal ceded loss functions in a class of increasing convex ceded loss functions. It turns out that the optimal ceded loss function is of stop-loss type.