Affine frequency division multiplexing (AFDM) has garnered significant attention due to its superior performance in high-mobility scenarios, as well as multiple waveform parameters that provide greater degrees of freedom for system design. This paper proposes a novel secure affine frequency division multiplexing (SE-AFDM) system, which enhances physical-layer security by dynamically varying an AFDM pre-chirp parameter across subcarriers and over AFDM symbols. In the SE-AFDM system, the pre-chirp parameter is dynamically generated from a codebook controlled by a long-period pseudo-noise (LPPN) sequence. Instead of applying spreading in the data domain, our parameter-domain spreading approach provides additional security while maintaining reliability and high spectral efficiency. We also propose a synchronization framework to solve the problem of reliably and rapidly synchronizing the dynamic parameter in fast time-varying channels. The theoretical derivations prove that unsynchronized eavesdroppers cannot eliminate the nonlinear impact of the time-varying parameter and further provide useful guidance for codebook design. Simulation results demonstrate the security advantages of the proposed SE-AFDM system in high-mobility scenarios, and the hardware prototype validates the effectiveness of the proposed SE-AFDM system and the proposed synchronization framework.