This paper presents a novel three-dimensional time-space cooperative guidance law against maneuvering target despite the presence of time-varying communication delays between missiles. The guidance law is divided into two parts. In the first part, a consensus protocol is designed for a multi-agent system consisting of a virtual leader and multiple followers. The objective is to tackle the problem of consensus convergence among the agents with communication delays. Additionally, the relationship between the upper bound of delays and the controller parameters is established. Based on the consensus protocol and a prescribed-time slide mode control method, the guidance law in the line-of-sight (LOS) direction is designed to ensure that the missiles attack the target simultaneously. In the second part, the multi-missile surrounding attack is achieved by designing different desired LOS azimuth and elevation angles for each missile. A guidance law in the normal LOS direction is designed based on the prescribed-time slide mode control method to ensure that the LOS angle converges to the desired values. To estimate the disturbances caused by the unknown and unpredictable acceleration of the maneuvering target in the LOS and normal LOS directions, fixed-time disturbance observers are designed. The stability analysis of the cooperative guidance law is provided in the appendix section. To demonstrate the effectiveness and superiority of the proposed cooperative guidance law, comparative simulations are performed.