The purpose of this paper is to propose a method of the calculations for position fix. The authors examine whether it is possible to utilize a method of optimization for calculating ship's position, however utilizing a method of least-squares for calculating ship's position has been studied. In this method position circles or position hyperbolas are utilized for positionfix and optimum ship's position is gained by solving basic equations for position fix. The features of this method are as follows; (1) No straight lines are used in place of position lines. (2) No directions of geographical positions or radio stations are necessary. Expected results are gained as the method is applied to position fix in celestial navigation.