Let be an absolutely continuous distribution having a density function with respect to the Lebesgue measure. The Shannon entropy is defined as . In this correspondence we propose, based on a random sample generated from , a nonparametric estimate of given by , where is the kernel estimate of due to Rosenblatt and Parzen. Regularity conditions are obtained under which the first and second mean consistencies of are established. These conditions are mild and easily satisfied. Examples, such as Gamma, Weibull, and normal distributions, are considered.