Through geomet ric observation , it is found that the nearest point on a curve is a tangent point between the curve and an off set curve of the other curve. Based on this observation , an off set method is presented for computing the minimum distance between two planar algebraic curves. The new method is geomet rically inst ructive , and can be used for computing the minimum distance between an algebraic curve and a parametric one on the same plane. For planar quadratic curves , the degree of the resulting univariate polynomial equation by our method is much lower than that of the equations in previous comparable methods , which may lead to lower computation complexity or higher robustness of the solutions.