The great circle sailing is composed of segments of rhumb line sailing in theory and practice. The waypoints along the great circle track are determined under the given initial conditions by the navigators. Since the conventional computation procedure of the great circle sailing, or called the computation procedure with reference to the vertex, is essentially an indirect method. A direct approach, based on the great circle equation (GCE) by using the vector algebra, is thus proposed to deal with the problems of the great circle sailing. In this newly developed approach, any point along the great circle track, such as the waypoints, vertex and the point crossing the equator, can be obtained effectively by using the derived different equations for different given conditions. Two computed examples are included to illustrate the proposed approach. In addition, because equations used in the same step of the conventional computation procedure may be different for relevant literatures, two evaluation criteria, error propagation and simplicity, are taken into consideration for improvement of the conventional procedure and an optimal computation procedure is further proposed for suggestion.