Born in Ulan Bator, Murun began playing soccer at age 12. He played for Mongolian Premier League clubsSelenge Press and Ulaanbaatar University from 2006–2008 and 2008–2009, respectively. He then played college soccer in the United States for the Hannibal-LaGrange University Trojans and the Central Methodist Eagles, both of the NAIA. In his one season at Hannibal-LaGrange, he tallied 1 goal and 2 assists in 11 matches. He scored his goal against the Truman Bulldogs on 3 November 2009. During his three seasons at CMU, he made 37 appearances and tallied 18 goals and 6 assists. He initially received an invitation to Hannibal-LaGrange after vying for a scholarship against 120 other candidates from Europe and Latin America. He signed a two-year contract with Krabi F.C. of the Thai Division 1 League in December 2013, becoming Mongolia's first ever professional footballer and one of the first footballers to play abroad. He made his debut for the club on 9 April 2014 in a Cup match against Khonkaen F.C., the club's rivals. Despite Murun scoring a goal in the match, Krabi was eliminated by the eventual 1–2 defeat. Between the opening match of the season in February and mid May, he made only two appearances for the club. He moved on loan to Satun United in May 2014 to secure more playing time and was Regional League South Division runner-up that season. He played his first match for Satun United on 10 May 2014 in a Cup match. He trained with Suphanburi FC of the Thai Premier League to become acclimated to the weather of Thailand before joining Krabi. Also prior to joining Krabi, he initially trialed with Rangsit F.C., also in Thailand, and Lao Toyota F.C. of the Lao Premier League. He was offered a professional contract by Lao Toyota but opted to join Krabi because of a preference to play in Thailand over Laos. He signed for Serbian First League club Mačva Šabac in March 2015 on a 1-year contract, becoming one of the first professional Mongolian footballers in Europe. He was signed by the club without a trial after he was recommended to Ivica Kralj by Dragan Anicic, head coach of FK BSK Borča, another Serbian team with which Murun trialed before FK Mačva Šaba. He trialed with three Serbian clubs in total. He also received invitations from clubs in Croatia and Bosnia and Herzegovina but did not attend because of visa and insurance issues. In January 2016, Murun returned to Mongolia and re-signed for Selenge Press FC after Mačva Šabac were relegated to the Serbian League. His contract was terminated because Serbian rules did not allow non-Serbian nationals to be on the roster of teams in the third division or lower. The player stated his return to the club was temporary while he searched for another professional club abroad. On 22 May 2016, he scored a goal in his first match back with the club, a 2–1 victory over FC Ulaanbaatar. In May 2016, Murun joined fellow Mongolian Premier League club Ulaanbaatar City.
International career
Murun represented Mongolia at the youth level, including matches against South Korea and North Korea for the U15 side. He made his senior international debut for Mongolia on 21 November 2007 in a 2010 FIFA World Cup qualifying match against North Korea. At age 16, he was the youngest player ever called up to the senior squad at the time of his debut.
