Homotopy methods are known to be effective methods for finding DC operating points of nonlinear circuits with the theoretical guarantee of global convergence. There are several types of homotopy methods; as one of the most efficient methods for solving bipolar transistor circuits, the variable-gain homotopy (VGH) method is well-known. In this paper, we propose an efficient VGH method where a more effective linear function is used in the homotopy function. By numerical examples, it is shown that the proposed method is more efficient than the conventional VGH method. It is also shown that the proposed method is globally convergent for modified nodal equations and can be implemented in SPICE easily without writing complicated programs.