To better understand the development of the fetal Autonomic Nervous System (ANS), estimation of Fetal Behavioral States (FBSes) is an essential parameter. The objective of this work is to use 1D CNN to classify FBSes into two states: quiet and active. Non-invasive electrocardiogram signals were collected from 105 healthy fetuses whose Gestational Age (GA) ranged from 20-40 weeks for a time between 3-10 min. Based on the fetal ECG signal, this study develops a 1D Convolutional Neural Network (CNN) for automatically obtaining features and identifying the behavioral state of the fetus. Our study employs a 1D CNN technique without extracting or selecting features from the fetal ECG signal. These networks can self-learn the distinguishing features of ECG signals. The proposed method for classifying fetal quiet states/active states provided an overall sensitivity, specificity, precision, and F1 score of 72.7/82.6%, 82.6/72.7%, 89.4/60%, and 80.2/69.5%, respectively. According to the results of this study, a deep learning approach combined with fetal ECG signals can be a useful pre-screening tool for fetal neurological assessment throughout gestation which has the advantage of reducing fetal mortality rate.