Abstract: The waverider has been the current research focus because of high lift to drag ratio in hypersonic state, while some deficiencies of waverider limit its practical application in engineering. Osculating-cone method is one of the most widely applicable waverider design methods for engineering, yielding much flexibility and efficiency. In order to remedy some of the deficiencies and improve the flexibility for waverider, the article extends the application of the osculating-cone waverider design method, conducting the geometric relationships among the inlet capture curve, flow capture tube and planform contour line, expressed by a differential equation set. The equation set lays a solid foundation for the planform-controllable waverider design. By introducing the numerical solving strategy for the differential equation set, combining with some solving tips, the osculating-cone waverider design by customizing the planform shape of leading edge is proposed. Three validation cases are generated in the article including the gradually varied leading edge, "S" leading edge and double swept planforms from the osculating-cone waverider by customizing the planfrom shape of the leading edge. Using computational fluid dynamics method, the flow fields of these three configurations are calculated and analyzed. Results suggested that the hypersonic wave-riding performance maintenances for the waverider since the shock wave obtained from CFD matches well with the design curve and high lift to drag ratio is remained as traditional waverider. The method and the CFD results indicate that it permit us to customize the planform of waverider conveniently and efficiently. The geometric relationships expressed by a differential equation set provide a novel idea to improve the flexibility and remedy some of the deficiencies of waverider.