Dempster-Shafer evidence theory (DST) is widely used in intelligent information processing, especially for information fusion. Recently, measuring the information volume in the framework of DST draws a lot of attention. Many theories and tools have been proposed to model the uncertain degree in DST, including Deng entropy. However, Deng entropy and the other uncertainty measures in DST pay no attention to the uncertainty in the frame of discernment (FOD) in the open world, which is the reason of this paper. To address this issue, Deng entropy is extended to the open world in DST framework. With the extended Deng entropy (EDE) in the open world, the uncertain information represented by FOD and the mass function of the empty set now can be properly modelled while measuring the uncertain degree in DST. EDE can be regarded as a generalization of Deng entropy in the open world and it can be degenerated to Deng entropy in the closed world if the mass value of the empty set is zero. A few numerical examples are presented to verify the applicable and useful of the new measure.