This study presents an single machine scheduling algorithm minimize lateness of product by controlling machining speed. Generally, production scheduling uses the information of process planning. But the production scheduling algorithm has not considered the control of machining speed in its procedures. Therefore, the purpose of this study is to consider the machining speed in production scheduling algorithm for efficient production scheduling. Machining time and machining cost required to manufacture a piece of a product are expressed as a unimodal convex function with respect to machining speed, so it has minimal point at minimum time speed or the minimum cost speed. Therefore, because of considering the machining cost, the control of machining speed for the algorithm is executed between minimum speed and maximum speed. An example is demonstrated to explain the algorithm.