In this paper, the finite-horizon filtering problem is investigated for a class of nonlinear time-delayed systems with an energy harvesting sensor. We consider a situation where the filter is located in a remote area from the sensor and the transmission of the measurements from the sensor to the filter may consume certain energy stored in sensor. The underlying sensor is capable of harvesting the energy from the environment. The transmission of the measurements is closely related to the sensor's energy level and, for the remote filter, the measurements are regarded as missing when the sensor energy is insufficient to maintain the normal communication between the sensor and the filter. In order to derive the missing rate of the measurements, the probability distribution of the amount of the sensor energy is calculated recursively at each time instant. Then, in the presence of parameter nonlinearities, time delays as well as the probabilistic missing measurements resulting from the limited capacity of the sensor, we design a finite-horizon filter such that an upper bound is guaranteed on the filtering error covariance at each time instant and the filter gain minimizing such an upper bound is subsequently obtained in terms of the solution to a set of recursive equations. Finally, a numerical simulation example is employed to demonstrate the effectiveness of the proposed filtering scheme. (C) 2018 Elsevier Ltd. All rights reserved.