Liver transplantation, which can be performed from either living-donors or cadavers, is the only viable treatment for end-stage liver diseases. In this study, we focus on living-donor liver transplantation. The timing of the transplantation from a living-donor is crucial as it affects the quality and the length of the patient's lifetime. The studies in the literature use risk-neutral Markov decision processes (MDPs) to optimize the timing of transplantation. However, in real life, the patients and the physicians are usually risk-averse, therefore, those risk neutral models fail to represent the real behavior. In this study, we model the living-donor liver transplantation problem as a risk-averse MDP. We incorporate risk-aversion into the MDP model using dynamic coherent measures of risk, and in order to be able to re ect varying risk preferences of the decision makers, we use first-order mean-semi-deviation and mean-AVaR as the one-step conditional measures of risk. We obtain optimal policies for patients having cirrhotic diseases or hepatitis B under different risk preferences and organs of different quality. We also measure the sensitivity of the optimal policies to the transition probabilities and to the quality of life. We further perform a simulation study in order to find the distribution of lifetime under the risk-averse optimal policies.