Path planning for field operation of agricultural machinery is an indispensible part for precision farming or autonomous field operation. In this study, two algorithms (I, II) of generating a time-based shortest operation path were suggested to plan an optimal operation of an agricultural tractor-implement in a rectangular shaped field. The algorithms were based on modification of a minimum spanning tree algorithm, and applied for tractor-implement operations. the generated path was consisted of round operation and returning operation sections. The number of round operation was determined from the condition that a tractor can turn smoothly at headlands. The performance of the algorithms was evaluated by the calculation number for path generation and the total path length generated. Their stability was affected by the number of returning operation, but the algorithm II was considered to be more stable. In addition, the performances of the developed algorithms were compared with those of the conventional field operations at selected field sizes and shapes. The results showed that the algorithms could reduce field operation time greatly. For a 100m$ imes$40m field, the reduced path length was 78m. The study also included an user interface program for implementing the algorithms and generating GPS coordinates that could be used in GIS softwares for precision farming.