In the high demand of the cloud computing environment, intrusion detection in a cloud network playing a big role in maintaining the faith of the client(s). Due to the increasing complexity of the cloud environment, the existing approaches which use the conventional neural networks are not able to utilise the relevant information from the network traffic, which leads to a low detection rate. This reduces the stability of the existing approaches in this changing environment. In this paper, an anomaly-based cloud intrusion detection system (IDS) is proposed for finding the intrusions in a cloud network. The proposed system uses a hybrid metaheuristic algorithm for feature selection and a deep learning approach for classification. For feature selection, grey wolf optimisation (GWO) is hybrid with a crow search algorithm (CSA), which extracts relevant features from the cloud network connection to be processed more effectively in the deep learning classifier section. A deep sparse auto-encoder (DSAE) is employed for the classification purpose. For the performance comparison, the considered metrics are accuracy, precision, recall or detection rate (DR), and F1 Score. Three publically well-known available datasets namely NSL-KDD, UNSW-NB15, and CICIDS 2017 have been considered for analysing the performance of the proposed GWO-CSA-DSAE model for intrusion detection in a cloud network. The experimental results of the proposed model have been compared with the results of existing recent approaches in the case of binary classification and multi-class classification. It is found that GWO-CSA-DSAE model is better for intrusion detection, which is the proposed model for intrusion detection in a cloud network.