Distributed multiple-input multiple-output (MIMO) dual-function radar-communication (DFRC) configuration, which is composed of multiple distributed dual-function transmitters, multiple radar receivers and multiple communication receivers, are capable of performing target state estimation and information transferring tasks simultaneously. In this article, the authors put forward a low probability of intercept (LPI)-based power resource allocation (PRA) scheme for the distributed MIMO-DFRC system. The key mechanism of the LPI-PRA scheme is to minimize the total power consumption of the overall system by optimizing the radiation power allocation of different dual-function transmitters subject to a predefined target parameter estimation accuracy for radar purpose and a certain wireless communication performance for communication purpose, leading to an improved LPI performance of the distributed MIMO-DFRC system. The closed-form expression for Cramer-Rao lower bound (CRLB) is derived to gauge the target position and velocity estimation performance, and the communication data rate (CDR) is adopted as the performance metric for data transmission. Subsequently, an efficient three-stage solution algorithm is put forward to tackle with the resulting constrained, non-linear, and non-convex optimization problem by exploiting the semi-definite programming (SDP) and Karush-Kuhn-Tuckers (KKT) necessary conditions. Simulation results demonstrate that the proposed LPI-PRA scheme is able to deliver superior LPI performance in terms of minimizing the total power consumption of the distributed MIMO-DFRC system, compared with other power resource allocation algorithms. (C) 2020 Elsevier Inc. All rights reserved.