An intrusion detection system plays an important role to ensure security in a mobile ad-hoc network (MANET). MANET does not have central administration that controls all nodes within the network. Due to the inherent characteristics of MANET, it suffers from various attacks such as packet dropping, denial of service, impersonation, and man-of-the middle, and other attacks. To protect MANET against such attacks, many researchers have proposed prevention, detection, and mitigation techniques. Since prevention techniques do not protect internal attacks, an intrusion detection system is preferred to detect both internal and external attacks. Previously, other scholars proposed several intrusion detection systems to classify as normal and abnormal activities. The existing traditional intrusion detection systems only consider data collection from individual layers. In addition, their performance is affected by the generated data size and the number of malicious nodes. Hence, the traditional intrusion detection systems may not be suitable for MANET environments. This research mainly focuses on the detection of packet-dropping attacks and normal behavior. The NS-3 simulator has been utilized for the generation of normal and the two packet-dropping attacks data including blackhole and worm-hole within MANET networks for 100 nodes. So, a dataset of 529,876 data point values with 42 features have been generated. A cross-layer-based anomaly detection system using deep learning algorithms is proposed. All experiments are performed on a Keras with 355,016 (67%) samples for training and 174,860 (33%) samples for testing. The extreme gradient boosting tree (Xgboost) and categorical boosting tree (Catboost) feature importance score with the threshold is used for feature selection. The proposed system was implemented using well-known classification techniques such as recurrent neural network (RNN), long short-term memory (LSTM), and gated recurrent unit (GRU). The performance of the algorithms was evaluated using classification metrics such as accuracy, confusion matrix, precision, recall, and f1-score and they have shown good performance. The experimental results showed that the proposed system using 35 optimal features gives 96.51%, 96.47%, 96.40 %, 96.17%, and 93.76% accuracy using LSTM, GRU, RNN, support vector machine (SVM), and random forest (RF) classifiers respectively. Moreover, the false alarm rates of LSTM, GRU, RNN, SVM and RF are 2.10%, 2.19%, 2.24%, 2.46%, and 3.71% respectively.