The recently developed affine frequency division multiplexing (AFDM) can achieve full diversity in doubly selective channels, providing a comprehensive sparse representation of the delay-Doppler domain channel. Thus, accurate channel estimation is feasible by using just one pilot symbol. However, traditional AFDM channel estimation schemes necessitate the use of guard intervals (GI) to mitigate data-pilot interference, leading to spectral efficiency degradation. In this paper, we propose a GI-free pilot-aided channel estimation algorithm for AFDM systems, which improves spectral efficiency significantly. To mitigate the interference between the pilot and data symbols caused by the absence of GI, we perform joint interference cancellation, channel estimation, and signal detection iterately. Simulation results show that the bit error rate (BER) performance of the proposed method can approach the ideal case with perfect channel estimation.