In weighted sum rule fusion, proper weights assignment for different biometric sources is very important. The effective weights assignment procedure based on individual score performance is the vital key in adaptive weighted sum fusion. In this paper, an adaptive user specific weighted sum based on score distance is devised to determine optimal weights. It integrates the performance of the biometric source represented by its Equal Error Rate (EER) and score distance in weights estimation procedure. Although the designated weighted sum fusion requires less setting and less exhaustive search of fusion parameters, it can obtain better performance than previous approaches. The proposed technique outperforms the existing user specific weighted fusion schemes in all experiments by consistently achieves a minimum EER value.