Lyudmila Chursina was born in Stalinabad (now Dushanbe; according to other sources, on the road during evacuation from Velikiye Luki to Stalinabad, near the village of Gruzdovo, Kunyinsky District, Kalinin Oblast). In 1959 she graduated from school with a gold medal in Velikiye Luki. She went to Moscow to enroll at the Moscow Aviation Institute. Together with a school friend, unexpectedly for herself, she was admitted to three theater schools at once: VGIK, GITIS, and the Shchukin Theater School. In 1963 she graduated from the B.V. Shchukin Theater School. For two years she served at the E.B. Vakhtangov Theater. From 1965 she worked at the Lenfilm film studio.

From 1974 she was at the A.S. Pushkin Leningrad Academic Drama Theater. From 1984 she was at the Central Theater of the Soviet Army. On March 11, 2014, she signed an appeal by cultural figures of the Russian Federation in support of the policy of Russian President V.V. Putin in Ukraine and Crimea. After filming in the picture "Donskaya Povest", she married the film's director Vladimir Alexandrovich Fetin (1925-1981). Her second husband was oceanologist and engineer at TsNIIMF Vladimir Petrovsky. Her third husband (1987-1991) was diplomat Igor Yuryevich Andropov (1941-2006), son of Yuri Vladimirovich Andropov (1914-1984). She has no children.