Affine frequency division multiplexing (AFDM) has recently emerged as a promising waveform for doubly-selective channles [1],[2], owing to its ability to fully exploit time-frequency diversity through appropriate tuning of the chirp-rate parameter [3],[4]. In [5], a direct-windowing-based pulse shaping transceiver was proposed for AFDM systems to suppress the Doppler sidelobes, thus improving the accuracy of channel estimation. Inspired by the theory of ``matrix equilibration" (Thm.~4.3 in [6]), we observe that the legacy AFDM pulse shaping method in [5] significantly increases the condition number of the effective channel matrix when path delay and Doppler parameters are randomly distributed, such ill-conditioning leads to the degradation in the solution stability of channel equalization under noisy conditions, thus resulting in the degradation of bit error rate (BER). To address this issue, this letter proposes a novel overlap-summation-based pulse shaping transceiver for AFDM systems (OS-PS-AFDM) to suppress the pulse sidelobes in the discrete affine Fourier transform (DAFT) domain, while maintaining the condition number of channel matrix, at the cost of time-domain prefix overhead. Consequently, the proposed OS-PS-AFDM transceiver simultaneously achieves accurate channel estimation and robust equalization performance. The source code of simulation is provided at https://github.com/SANIS-HITSZ/Waveform_AFDM.