The invention relates to a spiral-arc gear mechanism for parallel-shaft external-engaged transmission. The spiral-arc gear mechanism comprises a transmission pair consisting of a bull wheel and a pinion wheel, wherein the pinion wheel is connected with an input shaft, the bull wheel is connected with an output shaft, the axis of the pinion wheel and the axis of the bull wheel are parallel to each other, spiral arc grooves are uniformly distributed in the external surface of a cylindrical body of the pinion wheel, spiral arc teeth are uniformly distributed in the external surface of a cylindrical body of the bull wheel, both center lines of the spiral arc grooves and center lines of the spiral arc teeth are cylindrical helices, and the spiral arc grooves of the pinion wheel are matched with the spiral arc teeth of the bull wheel. When the pinion wheel and the bull wheel are mounted, one pair of spiral arc groove and spiral arc tooth is firstly enabled to be engaged with each other, a driver drives the input shaft and the pinion wheel to rotate, and thus, the external-engaged transmission between the two parallel shafts is realized; the shapes of the spiral arc grooves and the shapes of the spiral arc teeth can be determined by parameters, such as a transmission ratio, and a central line equation. The spiral-arc gear mechanism is simple and compact in structure, small in size, light in weight, high in strength and rigidity, high in contact ratio and high in single-stage transmission ratio and is suitable for being applied to the fields of small, micro and conventional machinery.