The theory and practice of water quality scoring and indexing are introduced. The monthly water analysis data are available for six stations long the down-stream Han River whthin the areal boundary of the Special City of Seoul. The data cover the period between 1975 and 1979 inclusive and contain the analytical findings on 37 water constituents including DO, BOD, temperature, total solids and etc. Sic parameters are selected form the 37 items, that, to the judgement of the writer, best reflect the water quality of the Han River. They are; dissolved oxggen saturation, pH, fecal coliform, total solids, BOD and nitrate+ammonia. For each of the six parameters, a subscore function is developed and graphically presented to facilitate the transform of a measurment of the arameter to a subscore on a common score(e.G. 0-100) The score of a sample is calculated as a fuction of the six subscores, using four different approaches; (1) the unweighted arithmetic water quality score, (2) the weighted arithmetic water quality score, (3)the unweighted multiplicative score and (4) the reduced (total) score. Independent of these calculated scores, the experts' score which is calculated by averaging the ratings of water quality experts is obtained and compared with each of the four calculated scores by means of the least square method. The experts' score compares most favorably with the "reduced" score with the correlation coefficient of 0.956 : therefore this method of water quality scoring is adopted to calculate the Han River water quality scores and indices. Water quality index data for Guiri, ukdo, Pokwangdong, Noryangjin, Yongdungpo and Kayang Stations, 1975-1979 are as follow: The overall water quality index data of the Han River between Guiri and Kayang Stations are found; 47.3 in 1976, 48.0 in 1977, 48.5 in 1978 and 54.7 in 1979, indicating the general trend towards water quality improvent in this part of the river, in terms of the increased water quality index by average 1.85 points per year during this period. Finally the optimum sampling frequencies distributed among the six stations, using an equation which takes into account the coefficients of variation of the water quality scores and indices arec calculated.alculated.