This paper investigates rapid cooperative guidance with finite time convergence in the context of missile attacks. Cooperative guidance systems play a crucial role in coordinating multiple missiles toward a common target efficiently in three-dimensional space. The missiles are assumed to be only able to exchange the time-to-go information with the neighbors based on an undirected communication network. A distributed guidance law called finite-time rapid cooperative guidance (Fit-RCG) is proposed. A nonlinear term is designed in Fit-RCG to ensure a faster convergence rate, and the finite time convergence is proved by using tools from graph theory and Lyapunov theory. Simulations are provided to validate Fit-RCG.