One can identify at least two types of inexactness: one is randomness associated with frequencies and the other is uncertainty associated with belief degrees. However, randomness and uncertainty usually exist in a complex system simultaneously. To model such complex phenomena, we present a concept of complex uncertain random variable. Then, we derive the complex chance distributions of complex uncertain random variables. Moreover, the expected value and variance of a complex uncertain random variable are also studied. Finally, we define and study the complex linear and normal uncertain random variables.