This paper deals with the design of a robust adaptive fuzzy nonsingular fast terminal sliding mode control strategy for the relative motion control of spacecraft in formation. A nonsingular terminal sliding surface, along with a fast reaching law, has been considered for fast and finite time convergence. Adaptive tuning algorithms are derived based on Lyapunov stability theory for updating the controller gains involved in the fast reaching law. In order to reduce the chattering, the discontinuous term in the reaching law has been replaced by a fuzzy inference mechanism. Lyapunov based adaptive tuning laws are derived for updating the fuzzy parameters involved. Numerical simulations based on nonlinear dynamics defined in leader centered Hill's frame, have been presented to prove the robustness of the proposed approach.