At the 2014 Junior Pan American Championships, Zeng swept all gold medals (all-around, hoop, ball, clubs, ribbon) and won USA a spot in the 2014 Youth Olympic Games; Later on, Zeng defended her junior title at the 2014 US Junior National championships, placing 1st (all-around, hoop, ball), 2nd (clubs), 3rd (ribbon). Zeng was selected as the sole representative of United States at the 2014 Youth Olympic Games in Nanjing, China. She placed second in the qualification and went on to take the all-around bronze in the finals with a total score of 56.750, just two hundredths behind Belarus’ Mariya Trubach who took the silver medal. Zeng’s medal marks the first rhythmic gymnastics medal for the U.S. at an Olympic or Youth Olympic Games. Moscow Grand Prix: In February 2015, Zeng made her senior and international debut competing at the 2015 Moscow Grand Prix finishing 21st in the all-around. USA Challenge: In March 6–7, Laura won 2015 Challenge Championship participated only by USA national team members. Lisboa World Cup: In March 27–29, Zeng competed at the 2015 Lisboa World Cup finishing 14th in the all-around. Pesaro World Cup: In April 10–12, she placed 11th in all-around among 56 competitors with a score of 68.40 at 2015 Pesaro World Cup in Italy. She also made Ribbon finals. Corbeil-Essonnes Tournament: In May 8–10, she competed at the Corbeil-Essonnes International Rhythmic Gymnastics Tournament and finished 3rd in all-around behind Russians  Arina Averina and Dina Averina, she qualified to 3 event finals and won silver in clubs, bronze in ball and placed 4th in ribbon. USA Nationals: In June 25–27, Zeng won the all-around title as a first year senior in USA Nationals 2015 ahead of Jasmine Kerber. In apparatus finals, she won in Hoop, Clubs, and Ribbon titles. Pan American Games: At the 2015 Pan American Games in July 15–20, Zeng swept the gold in the all-around with a total score of 64.575 points and all the apparatus finals, becoming the second American to win the all-around and all the apparatus finals at the Pan American Games since Mary Sanders in 2003. Zeng was the most decorated athlete for the Pan Am Toronto.