In general stars are known to be sinks of Li as this light element gets destroyed at about couple of million degree Kelvin. Contrary to this general understanding Li has been found anomalously high in a small group of red giants. In some cases, Li abundance is a factor of 10 more than the interstellar medium value of A(Li) ~3.2~dex and 100 - 1000 times more than the standard model predictions of maximum abundance of A(Li) ~1.5~dex for RGB giants. In this talk, I will discuss the problem and our observational efforts to find its origin.