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Smart noise jamming forms active jamming by intercepting, modulating, and forwarding radar signals into the radar receiver, which seriously affects the radar range recovery performance. In this paper, we propose a novel waveform design approach and an efficient range recovery method for high-resolution radar in the jamming scenario. Firstly, we propose an intra-pulse frequency-coded frequency-modulated continuous waveform (IPFC-FMCW), which contains multiple FMCW chips with different widths and frequencies, to combat the smart noise jamming. After the jamming suppression, the proposed waveform has a low sidelobe level, which is different from traditional FMCW signals for which the observations are periodically missing, resulting in high sidelobe levels. Then, to improve the range recovery performance of the waveform after jamming suppression, we optimize the range profile by designing the transmit waveform and then solve it by a simulated annealing algorithm. Next, based on the designed waveform, we derive the echo model after jamming suppression and propose a gridless compressed sensing (CS) method to recover the range of the targets. Compared with the existing waveforms and methods, the proposed waveform and the processing method achieve better range recovery performance in the jamming scenario. Numerical simulations are utilized to demonstrate the range recovery effectiveness of the proposed waveform and method in smart noise jamming.