A performance index is very important and indispensable to the evaluation of automatic steering system of ships in open sea from the viewpoint of energy saving. In this paper, we derive the performance index of automatic steering system from the concept of energy loss of propulsive power. The index is found to consist of three terms, energy loss due to elongation of sailing distance, energy loss due to steering, and energy loss due to yawing motion. We also provide two kinds of calculation method on the performance index ; frequency response analysis and digital simulation. The numerical calculations are carried out for an ore carrier and a fishing boat by both methods. The frequency response analysis is found to be useful if the system is linear and the disturbance on ship is not large. If the system is nonlinear or the disturbance is excessive, the method of digital simulation has to be applied for the accurate evaluation of the performance index. Further investigations into the effects of nonlinear elements such as weather adjuster, power unit etc. on the performance index, will be dealt with in another paper.