Source localization is of great importance for wireless sensor network applications. Locating emission sources using received signal strength (RSS) measurements is investigated in this paper. As RSS localization is a non-convex optimization problem, it is difficult to achieve global optima. Many optimization methods have been proposed to relax it to a convex optimization problem. Unlike these methods, we propose a convex combination scheme. By introducing a highly accurate linear approximation of a logarithmic function, the source location is represented by a convex combination of a set of virtual anchors. Then the original problem is relaxed to be a convex optimization problem of finding the optimal combination coefficients, which can be solved efficiently using constrained least squares. To obtain the virtual nodes, we construct parallel lines and use their intersections to form a convex polygon, which covers the source location with certain probability. The vertices of the polygon are taken as the virtual nodes. Numerical examples verify the performance of the proposed method in both localization accuracy and computational efficiency.