Accurate estimation of the apparent diffusion coefficient (ADC) of lesions in diffusion-weighted magnetic resonance imaging (DWMRI) is important to predict and monitor anticancer therapy response. The task of ADC estimation of lesions is complicated due to noise in the image, different variances in signal strengths at different b values and other random phenomena. In organs that have visceral motion, due to motion across scans, estimating the ADC becomes even more complex. To get rid of inaccuracies due to motion, only a single ADC value of the lesion is estimated, conventionally using a linear-regression (LR) approach. The LR approach is based on an inaccurate noise model and also suffers from other deficiencies. In this paper, we propose an easy-to-implement and computationally-fast maximum-likelihood (ML) method to estimate the ADC value of heterogeneous lesions in visceral organs. The proposed method takes into account the Rician distribution of noise in DWMRI. In the process, we also derive the statistical model for the measured mean signal intensity in DWMRI. We show using Monte-Carlo simulations that that the proposed method is more accurate than the LR method.