In this paper, new nonsingular terminal sliding mode control guidance laws (NTSMCGLs) to unknown maneuvering target intercept are proposed and their finite-time convergences are proved. A novel nonsingular terminal sliding mode surface based on a predefined angle is designed to improve intercept performance and avoid singularity problem. The presented guidance law requires no information on maneuvering target that is estimated and compensated by extended state observer (ESO), and it can be used in practical systems where the target can evade freely. Also, undesired chattering is restrained effectively by real-time estimation and compensation of ESO. Simulation results show that the NTSMCGLs can achieve exact interception.