[3] After first studying Chinese dance and ballet, Zeng started rhythmic gymnastics at age seven after her friend told her about it.

[4] In 2018, Laura graduated from high school as a National Merit Scholar Finalist and committed to Yale University.

[13] She then competed in the Dundee Cup in Sofia, Bulgaria and won the all-around bronze medal behind Aleksandra Soldatova and Zhena Trashlieva.

[17] She then competed at the Gymnastik Schmiden International in Fellbach, Germany winning gold in all-around, hoop, clubs, ribbon and bronze in ball.

[23] At the 2014 Junior Pan American Championships, Zeng swept all gold medals and won the United States a spot at the 2014 Youth Olympic Games.

[24] She then traveled to Minsk to compete at the Crystal Rose Junior Tournament where she won team gold, ball and ribbon silver, and hoop and clubs bronze.

[26] Zeng was selected as the sole representative of United States at the 2014 Summer Youth Olympics in Nanjing, China.

[40] Zeng was selected to compete in her first World Championships in Stuttgart alongside Jazzy Kerber, Camilla Feeley and Serena Lu.

[47] A couple of weeks later she competed at the Lisbon World Cup where she finished seventh in the all-around with a total of 70.150 points and qualified for three event finals placing eighth in clubs and hoop and fifth in ball.

[52][53] Prior to the Olympic Games, Zeng finished eleventh all-around, sixth in hoop, and fifth in clubs and ribbon at the Kazan World Cup.

[56] Zeng's first competition after the 2016 Olympic Games was the Rhythmic Challenge in Indianapolis, Indiana where she won the all-around gold medal.

[58] She qualified for all four event finals and earned her third and fourth career World Cup bronze medals in hoop and clubs and also finished seventh in ball and ribbon.

[71] In April, she competed at the Baku World Cup and won the hoop bronze medal in a tie-breaker with Boryana Kaleyn behind Russia's Mariia Sergeeva and Belarus's Katsiaryna Halkina.

She provided evidence to the United States Anti-Doping Agency (USADA) that she was prescribed an altitude sickness medication containing acetazolamide while on vacation in Machupicchu, Peru believing it was ibuprofen.

[80][81] Zeng began her 2019 season at the Tashkent World Cup where she placed eighth in the all-around and clubs and sixth in ball.

[83] Then in May, she placed sixth all-around, fourth in hoop, fifth in ball, and eighth in clubs at the Guadalajara World Challenge Cup.

[84] She won another hoop bronze medal at the Brno Grand Prix and placed fifth in ribbon and tenth in all-around.

[86] She won the all-around bronze medal at the Summer Universiade behind Ekaterina Selezneva and Zohra Aghamirova, and she also finished fourth in the hoop, ball, and clubs final.

[88] At the World Championships in Baku, Azerbaijan, the American team of Zeng, Evita Griskenas, and Camilla Feeley placed seventh.

[99] Zeng won the all-around at the 2021 USA Gymnastics Championships and was selected to represent the United States at the 2020 Summer Olympics.

[100] Before the Olympics, she competed at the Israel Grand Prix in Tel Aviv where she placed sixth in clubs and seventh in all-around, hoop, and ball.

[101] At the 2020 Olympic Games in Tokyo, she finished thirteenth in the qualification round for the individual all-around and was the third reserve for the final.