In mobile radio propagation, the variation in the local mean power is called shadow fading (or slow fading). It has been observed experimentally that the distribution of shadow fading is approximately lognormal over a wide range of propagation environments, carrier frequencies, and receiver-transmitter distances, although the exact reason for this remains somewhat unclear. In this paper we model the received signal as a superposition of plane waves with random powers. It is shown that if the sum of the plane wave powers satisfy central limit theorem, the received signal will have approximately lognormal distribution. The result offers a novel explanation for the lognormality of shadow fading.