To solve the problems of poor real-time tension tracking, large overshoot, long adjustment time, and large tension fluctuation error that exist in the current control system for yarn feeding in the circular weft knitting machine, this paper presents an optimized and improved adaptive genetic algorithm (AGA) for adjusting the PID (Proportional Integral Derivative) parameters of the tension control part of the yarn-conveying system (AGA-PID). The algorithm is combined with the field-oriented control technology of the permanent magnet synchronous motor to design a closed-loop control strategy for the yarn-conveying system of a circular weft knitting machine. The MATLAB-Simulink simulation model was used to analyze the external tension loop-based AGA-PID controller and permanent magnet synchronous motor dual closed-loop control strategy of the yarn transport control system. The experimental verification was conducted by constructing an experimental platform that simulates the real process of yarn transportation. The outcomes of system simulations and experiments have consistently demonstrated that the AGA-PID control algorithm outperforms the GA-PID and PID control algorithms in terms of overshooting, response speed, stability, and anti-jamming ability. The yarn transport control system, which is designed to operate based on an AGA-PID control algorithm, is capable of reducing the fluctuations in tension that occur during the transportation of yarn and exhibits enhanced control accuracy, effectively stabilizing yarn tension control during the conveying process. The application of this algorithm can enhance the overall elasticity uniformity and surface flatness of knitted fabrics, thereby facilitating the realization of adjustable and controllable local elasticity in fabrics.