This paper introduces a secure affine frequency division multiplexing (SE-AFDM) for wireless communication systems to enhance communication security. Besides configuring the parameter c1 to obtain communication reliability under doubly selective channels, we also utilize the time-varying parameter c2 to improve the security of the communications system. The derived input-output relation shows that the legitimate receiver can eliminate the nonlinear impact introduced by the time-varying c2 without losing the bit error rate (BER) performance. Moreover, it is theoretically proved that the eavesdropper cannot separate the time-varying c2 and random information symbols, such that the BER performance of the eavesdropper is severely deteriorated. Meanwhile, the analysis of the effective signal-to-interference-plus-noise ratio (SINR) of the eavesdropper illustrates that the SINR decreases as the value range of c2 expands. Numerical results verify that the proposed SE-AFDM waveform has significant security while maintaining good BER performance in high-mobility scenarios.