To reduce the missing rate caused by the arching phenomenon of seed potatoes in the traditional seed boxes of cup-belt potato planters, a conical-shaped seed box comprising a seed-metering box and a reseeding box connected together was proposed. The method in this paper combined the discrete-element-analysis method and response-surface method and took the movement of the seed-potato group in the seed box as the research object. First, by analyzing the force and speed of seed potatoes, the main structural parameters affecting the seed-box seed-metering performance were determined, and the indices for evaluating the seed-box seed-metering performance were established. Additionally, a single-factor simulation test and orthogonal test were carried out for the main structural parameters of the seed box. Using the optimized structural parameters of the seed box, a trial conical seed box was produced, and bench-verification tests were carried out. The results showed that the multiple rate, missing rate and coefficient of the variation of the plant distance for the conical seed box were reduced by 4.76%, 4.0% and 9.18%, respectively. The research results have practical significance as guidance for improving the sowing performance of cup-belt potato planters. At the same time, the research results have reference value for solving the arching problem for granular materials in the box.