Ultra-reliable and low-latency communications (URLLC) is a critical requirement for Beyond 5G (B5G) and 6G vertical applications. However, URLLC scenarios seriously restrict packet length in the physical layer, which makes it difficult to exploit both time/frequency diversity and degrades transmission reliability. Cell-free massive MIMO (mMIMO) is a promising technology that can provide sufficient antennas for space diversity to fulfill the high reliability demands and improve the performance of cell-edge users. In this article, we propose a short packet transmission scheme in a cell-free mMIMO system for URLLC scenarios. To mitigate inter-user interference and pilot contamination, we employ zero-forcing combining and propose a pilot assignment algorithm. The closed-form expressions for performance metrics are derived and used for joint power allocation to enhance the performance of users located at the cell-edge or those experiencing strong interference. The simulation results confirm the tightness between the closed-form performance metrics and Monte Carlo simulations. Furthermore, the effectiveness of the proposed pilot assignment algorithm and joint power allocation method has been successfully verified.