This paper presents a new effective measure of uncertainty (MoU) of basic belief assignments. This new continuous measure is effective in the sense that it satisfies a small number of very natural and essential desiderata. Our new simple mathematical definition of MoU captures well the interwoven link of randomness and imprecision inherent to basic belief assignments. Its numerical value is easy to calculate. This new effective MoU characterizes efficiently any source of evidence used in the belief functions framework. Because this MoU coincides with Shannon entropy for any Bayesian basic belief assignment, it can be also interpreted as an effective generalization of Shannon entropy. We also provide several examples to show how this new MoU works.