In this paper, a new adaptive nonsingular terminal sliding mode control theory based impact angle guidance law for intercepting maneuvering targets was documented. In the design procedure, a new adaptive law for target acceleration bound estimation was presented, which allowed the proposed guidance law to be used without the requirement of the information on the target maneuvering profiles. With the aid of Lyapunov stability criteria, the finite-time convergent characteristics of the line-of-sight angle and its derivative were proven in theory. Numerical simulations were also performed under various conditions to demonstrate the effectiveness of the proposed guidance law.