The accurate evaluation of nearly singular boundary integrals is an important issue in boundary element analysis, and the importance of this problem is next to the singular boundary integrals. Although many ways of evaluating nearly singular integrals have been developed in recent years, and obtained varying degree of success, questions still remain. In this paper, a new efficient transformation is proposed, based on a new idea of transformation with variables. The proposed transformation can remove the near singularity efficiently by smoothing out the rapid variations of the integrand of nearly singular integrals, and improve the accuracy of numerical results of nearly singular integrals greatly without increasing the computational effort. Numerical examples of potential problems are given, with results, showing the high efficiency and the stability of the suggested approach, even when the internal point is very close to the boundary.