This paper proposes a deep learning method for epicentral distance estimation using a single-channel seismic waveform. The model is based on a convolutional recurrent neural network structure to extract spatial and temporal features. Since the proposed model needs only single-channel data, it can also perform the distance estimation even when some channels of the sensor are adversely disabled. To evaluate our approach, we conduct distance estimation experiments with the Korean peninsula earthquake database from 2016 to 2018, which include microearthquakes and distant earthquakes. The epicentral distance estimation by the proposed method show an absolute mean error of 0.50 km with 9.16km standard deviation of error distribution, which shows the best estimation result among the competing model structures. The promising result indicates that the proposed approach can be deployed for epicentral localization task as part of realizing a robust earthquake monitoring system.