Purpose The modern manufacturing industry has put forward higher requirements for the assembly accuracy of components with the development of the industrial technology. For precision assembly, the traditional assembly process study based on tolerance has had difficulty in meeting these requirements. Hence, the distribution of the form errors must be considered. The registration between the two mating surfaces with form errors determines the parts’ assembly position, and is the basis for the prediction and control of the assembly accuracy. This study aims to provide a new surfaces registration method which takes form errors into consideration. Design/methodology/approach This study presents a new registration approach based on the minimum potential energy. A unique set of contact points on mating surfaces that meet the actual conditions can be obtained and the spatial position of the assembled part is calculated. Findings The experimental results show that the calculated values are in good agreement with the experimental values. Furthermore, the root mean square error is within 2%, which proves the validity and accuracy of the approach. Originality/value This paper provides an effective and new method for precision assembly which takes form errors into consideration. The method can give the optimal solution of the contact points, which is more consistent with the actual assembly situation and provides a basis for predicting assembly accuracy.