Kim scored a team-high 22 points in the 25-22, 26-24, 25-21 bronze-medal match defeat to Japan on Saturday at Earls Court. Her points total was three points better than the 204 points scored by Ekaterina Gamova of Russia at the 2004 Athens Games.
Logan Tom of the United States led scoring in Beijing four years ago with 124 points.
"It's really great, this gives me a lot of pride and confidence for my career," said the 24-year-old Kim, who scored 186 points from spikes, 14 from blocks and seven from serves in eight matches.
South Korea missed out on its first Olympic medal since winning bronze at the 1976 Montreal Games. Japan won its first women's volleyball medal since a bronze at the 1984 in Los Angeles with the help of Saori Sakoda's game-high 23 points.
Kim's Olympics breakout certainly established South Korea as a team to watch come Rio de Janeiro in four years as she helped guide the Asian nation back to the games for the first time since Athens.
"I believe that throughout this tournament the level of (South) Korean volleyball has gone to the next level," Kim, playing in her first Olympics, said through an interpreter. "There are some areas that we did well and other areas we didn't do very well but in those areas where we struggled we will try to improve ourselves for next time and areas we did well we will try to build on."
South Korea's performances — they beat Brazil, Serbia and Italy — were encouraging considering the team finished 13th at the 2010 World Championship and 14th at this year's World Grand Prix.
"Since last year's Grand Prix, Kim Yeon-koung has become very well known and since playing in the Turkish league she has experienced international volleyball," coach Kim Hyung-sil said through an interpreter.
So while Kim appreciated the Olympic honour, she admitted the team's inability to stay composed cost it bronze.
"The referee's decisions broke our momentum so that ended up breaking our morale and that's why we couldn't play as best as we hoped," the 1.92-meter (6-foot-4) wing spiker said. "I'm really disappointed because we couldn't show all the good play that we are capable of."