The paper proposes a joint semi-blind algorithm for simultaneously cancelling the self-interference component and estimating the propagation channel in 5G Quasi-Cyclic Low-Density Parity-Check (QC-LDPC)-encoded short-packet Full-Duplex (FD) transmissions. To avoid the effect of channel estimation processes when using short-packet transmissions, this semi-blind algorithm was developed by taking into account only a small number (four at least) pilot symbols, which was integrated with the intended information sequence and used for the feedback loop of the estimation of the channels. The results showed that this semi-blind algorithm not only achieved nearly optimal performance, but also significantly reduced the processing time and computational complexity. This semi-blind algorithm can also improve the performances of the Mean-Squared Error (MSE) and Bit Error Rate (BER). The results of this study highlight the potential efficiency of this joint semi-blind iterative algorithm for 5G and Beyond and/or practical IoT transmission scenarios.