A new method, is presented the ordinal wavefront reconstruction method to calculate minimum traveltimes and ray paths. In the previous traveltime calculation methods the source is taken as center and the calculation is made layer upon layer and step by step. It would result in acquiring half-baked wavefront information. In this paper, the ordinal wavefront reconstruction method is used in calculating minimum traveltimes according to actual wavefront surfaces' order. The calculating strategy is to take calculation point as center. The fore-node coordinate of the minimum traveltimes of the calculating point is logged directly, at the same time, the minimum traveltimes and ray paths are calculated. This is a kind of synchronous global algorithm. This method has its advantages, such as simple principle, easy implementation, no limit by different velocities, and fast computation etc.. The numerical experiments show that the ordinal wavefront reconstruction method has higher calculation precision and running efficiency.